Abid Ali fell for a duck in just the second over of the day, and Pakistan were looking shaky when Pope snared the scalps of ul-Haq and Haris Sohail (two) shortly before lunch.
Masood, Azam, and Shafiq helped drag Pakistan out of trouble, but Pope continued to pick up wickets at regular intervals.
Azam, who scored 157 against a powerful Australia A squad earlier in the week, was on track for another big score before becoming Pope’s fourth victim.
But Shafiq, who scored 119 earlier in the week, was able to keep Pope at bay.
Pope burst onto the scene as an 18-year-old last year when he snared 7-87 in just his second first-class game.
The flame-haired spinner hasn’t played a Shield game this summer, but his performance against Pakistan is sure to put him back in the selection mix for South Australia.
“It’s pretty awesome,” Pope said of his success against Pakistan.
“Five-for in any format against anyone is a bowler’s dream. I was very privileged and happy to get it today, especially on a fast bowler’s wicket.
“It’s nice it turned a little bit, and there were some good catches from the boys.”
Pakistan are using the match as their final warm-up ahead of the first Test against Australia, starting on Thursday at the Gabba.