Rasheda Ali was born too late to see her father in the arena in all his swaggering pomp but, thanks to the magic of film, the quick step, verbal taunts and regal bearing of Muhammad Ali never fade. “I watch him boxing all the time because he was so good at it,” she says. “It was like watching a Shakespearean actor. He was so beautiful when he moved.

“I don’t see that today. My dad had so much passion for the sport; he loved it so much. The earlier years in his prime, it was wonderful to watch him dance around the ring. It’s something that I don’t think we’ll ever see again.”

Ali died five years ago this week. A documentary film, City of Ali, marks the anniversary by exploring the place where he was born and, 74 years later, buried with much fanfare: Louisville, Kentucky. Directed by Graham Shelby, it tells how Ali grew up in the era of Jim Crow racial segregation and, when he refused to fight in the Vietnam war, faced widespread hostility.

But as the decades passed, the three-time world heavyweight champion became a legend in his own lifetime – a comic depicted him boxing Superman – as well as a lodestar of civil rights, a Muslim who preached interfaith tolerance, a sufferer of Parkinson’s disease whose courage and charisma burned bright. In June 2016 Louisville gave “the greatest” a funeral worthy of a king, with more than 100,000 people lining the streets and tributes by everyone from Bill Clinton to Billy Crystal.

To Rasheda, who shares his Muslim faith, he was always Dad, playing the clown at home just as he did on camera. “Parts of this film made me cry tears of joy,” the 50-year-old says via Zoom from home in Las Vegas. “I had sadness, too, because I remembered watching my dad and how funny he was and how he made people laugh. My dad was like that with us. He loved to play pranks on us and he did magic tricks for my children, his grandkids.”

She fondly recalls family outings to the cinema – but only after bribing him to take his Parkinson’s disease medicines. “I told him we were going to go see Peter Jackson’s King Kong and showed him the trailer and his eyes blew up and he was like, ‘Oh, my God, I’m going to go see that movie.’ I said, ‘Daddy, we can’t see the movie unless you take your medicine.’ So he took his medication reluctantly and we got out of the house.

“Daddy loved to watch his people. He loved to see their expressions when he walked in a room. So we went to the movies and he had all of these people crowding and my dad loved being Muhammad Ali. He loved hanging out with his fans and he loved taking us with him and bragging. He would take all of his girls and we’d get in a car and we’d drive around town.”

Ali had seven daughters and two sons. Rasheda’s continued sense of closeness to him radiates from the film and from Zoom. “I would talk to my dad secretly about things that I couldn’t share with my friends,” she says. “My dad was very candid and he was a worldly man so I could talk to him about things that were kind of personal that I was embarrassed to tell even my friends.

“I could tell him about things that I was uncomfortable with. I was struggling with my own personal issues and he would always just give me his best words of advice, like it doesn’t matter how old you are, it doesn’t matter what your situation is, if you believe that you can do something, you just do it. It resonates with me even to this day.”

Born in Louisville as Cassius Marcellus Clay, he announced his conversion to Islam in 1964 and changed his name to Muhammad Ali (some older residents of the city never quite accepted it). Rasheda insists that his formal diagnosis with Parkinson’s disease in 1984, three years after he retired from boxing, did not weaken his own faith.

“It had to have been hard for him to be diagnosed with something that there is no cure for. It was probably mind-boggling and shocking at first but, once my dad was able to accept his condition, he embraced it and he always felt that everything happens for a reason. God put him on this earth for a reason; God gave him this condition for a reason.

“He didn’t stop giving to people. He didn’t stop sharing. It was a little difficult at the end when it was hard to walk and talk but he still continued to do the things that he thinks God put him on this earth for: to give to others. In my honest opinion, I think that Parkinson’s disease saved his life.”

Rasheda, an advocate for research into the progressive nervous system disorder and author of a children’s book about it, explains: “Parkinson’s disease is a very humbling experience, something that takes away: my dad’s best asset was his speech and this was a test to see how much faith that my dad had. In our religion, we feel that when you’re tested, it doesn’t mean you’re a bad person, God just loves you and wants to see how much we love the Almighty.

“I think my dad embraced Parkinson’s in the sense where he felt that, ‘This is God testing me to see if I will still have faith in him, even though it’s harder for me to talk and walk.’ I personally think that it put him on another level spiritually, because I think he handled that very, very complicated condition very well considering.”

After years of keeping a low profile, Ali, a trembling but indomitable colossus, returned to the public stage by lighting the Olympic flame at the opening of the 1996 games in Atlanta. His left hand shook uncontrollably. His right held the torch aloft.

Rasheda sounds emotional at the memory: “That was very brave of him and he did that not just for himself but for other people who had that condition. He wanted to let these people know that ‘I’m Muhammad Ali, I have Parkinson’s but I can still be great and I can still do things that will shake up the world.’ He gave people with other conditions the ability to be brave and strong and hold on, because that’s what he did. He held on to his faith.”

Rasheda’s sister, Laila, was a professional boxer who retired unbeaten and now Rasheda’s son, Nico, 20, has just turned pro. Sounding like any worried parent, she acknowledges: “I understand why, because he had a connection with his grandfather and then he just started loving the sport. I’m not 100% happy with it but I’m supporting him 100%.”

Ali’s death came amid growing unrest over police shootings of unarmed African Americans and a presidential election campaign between Hillary Clinton and Donald Trump, who was proposing a ban on Muslims entering the US. Rasheda reflects: “My dad’s movement, and Malcolm X and Martin Luther King and their stance against police brutality back then, is coming full circle because we’re seeing it all over again.

“My dad had gone through hate crimes. He’d gone through tons of death threats. Islamophobia was on the rise at the time of my dad’s death. There was a heated presidential campaign so there were a lot of people coming out of the woodwork: hate groups and the like against African Americans, people of colour, Jewish people, Muslims.

“It was just really overwhelming. I think my dad’s stance against these type of hate groups resonates and definitely was a huge inspiration to the Black Lives Matter movement.”

Trump, who hosted big fights at his casinos, had appeared at Ali’s charity events, while Ali attended Trump’s wedding to Melania Knauss at his Mar-a-Lago estate in Florida in 2005. When Ali died, the businessman turned candidate told the New York Times that Ali was a “terrific guy”, “so generous” and an “amazing poet”.

Trump went on to win election a few months later and, as president, quickly issued a travel ban targeting seven Muslim-majority countries. Rasheda, who recalls meeting Trump briefly but does not know him well, says: “He was a huge fan of my father but then, once he got in office, I think he forgot who my dad was.

“You can’t be a fan of someone and go against his religion and his beliefs. Once he got into office, he had a different political agenda and he decided that he wanted to cater to people that didn’t like Muslims and didn’t like African Americans or Jews or any other group. Unfortunately, the political agenda became more important than the love of people.”

She continues: “My dad was very clear about who he embraced and he always really embraced those who loved others. So my dad would not have been for anyone who excluded especially a group of Muslims. He always believed in implementing love and inclusion and he always was against racial inequality from the start because of what he grew up in.”

City of Ali briefly raises the question of whether Ali might have been buried in Mecca but he chose Louisville, the city that made him and is his parents’ resting place. Rasheda, who grew up in Chicago, came to know it as a child from visiting her grandparents and other family members. She still goes back to visit the Muhammad Ali Center and stand at her father’s grave.

“When I go to Louisville, I bring flowers to him. I get my alone time with my dad so I can talk to him and reflect, tell him what I’m doing, what I’m working on. I always cry because I miss him and that’s not going to stop, even in the near future. It’s not going to change because I miss him every day and he was a big part of our lives.”

She adds wistfully: “Times I spent with him, they’re like gold. Even a moment alone with him was like gold because we shared him so much with everyone else. It was really nice to be able to have that quiet alone time with him. It was a gift.”

• City of Ali is available to rent digitally in the US with a UK date to be announced