Ellie-May asked "why won't the doctor see me?" before returning to the family home in Malpas, Newport, where she went to bed at 8pm.
Clark heard her daughter coughing at 10.30pm and called an ambulance after finding her struggling to breathe, with her hands and face blue.
The little girl died shortly after arriving at the Royal Gwent Hospital.
Ellie-May's inquest in Newport heard Rowe had previously received a letter from a consultant stating that the little girl was at risk of having "an episode of severe/life threatening asthma".
Rowe did not ask the reason behind Ellie-May's emergency appointment, or look into her medical notes before refusing to see her.
Rob Sowersby, representing Ellie-May's family, told the inquest: "Dr Rowe made a clinical decision without any clinical information whatsoever.
"She sent away a 5-year-old patient from an emergency appointment without even opening her records.
"Dr Rowe agreed that when she opened the letter from the hospital, stating that Ellie-May was at risk of serious/life threatening asthma, she should have recorded that prominently on Ellie-May's clinical record.
"If she had done that, then that would have been obvious to her when the clinical records were opened."
Sowersby said Ellie-May's mother was "sure" that the steroids usually provided to treat the girl when she attended the surgery would have helped as they had in the past.
"There is no reason to suggest they wouldn't have worked this time," Sowersby said.
Clark told the inquest that Ellie-May began suffering with a wheezy chest and was first admitted to hospital in November 2011, two months before her second birthday.
She was prescribed inhalers but returned to hospital every three to four months. The last admission before her death was in March 2014.
Ellie-May was off school for four days and went to the surgery on January 22 because of her wheezing.
Clark said her daughter was wheezy when she collected her from Malpas Court Primary School at 3pm on January 25.
She carried her crying daughter to her mother's house and phoned the doctor's surgery at 3.30pm to request a home visit.
A receptionist phoned back at 4.35pm and booked Ellie-May for an emergency appointment at 5pm. Clark immediately warned she might be late.
Clark, who had an 8-week-old baby at the time, said she arrived at the surgery at 5.05pm and waited in line to speak to the receptionist.
Receptionist Ann Jones phoned Rowe but was told that Ellie-May had to return for an appointment in the morning, as she was late.
"We got outside and because I was angry, I got upset," Clark said. "When Ellie-May saw me upset she started getting upset.
"She said 'why won't the doctor see me?'."
Clark returned home with her daughter, checking her on every 10-15 minutes, giving her an inhaler every 30 minutes or so.
She heard Ellie-May coughing at 10.30pm and went into her bedroom to give her an inhaler.
"She fell off her bed onto the floor," Miss Clark said. "I turned her light on and I saw her hands and her face were blue. I rang 999 straight away."
Rowe had no appointments between 4.50 and 5.20pm but did not check Ellie-May's notes and was seeing another patient when Jones phoned to say that she had arrived.
"She said that she had arrived and she said 'I'll tell her to come back tomorrow morning, shall I?' and I said 'yes'," Rowe said.
The inquest heard Rowe could have asked another doctor to see Ellie-May, could have seen her after her patient had left and could have spoken to the doctor who arranged the emergency appointment for her.
When asked why she had not, Rowe replied: "I don't know. I was busy seeing to the other patient that I had with me."
She confirmed she would have acted differently if she had seen Ellie-May's notes or the reason for the appointment.
When asked about the "10-minute rule", Rowe said: "If you have 25 patients to see in a morning or afternoon and a lot of people are 15 minutes late or 20 minutes late you are never going to be able to manage your work."
A post-mortem examination by Dr Andrew Bamber found Ellie-May had died from bronchial asthma and may have suffered a seizure before her death because of a lack of oxygen.
