Most plant species have hardiness limits--that is temperature extremes beyond which they can not survive.  These limits vary greatly from one species to another depending upon their adaptation to a particular locale or climate.

The following publication describes ways these limits were expressed following Texas' extreme cold spell last winter.

https://www.lubbockonline.com/story/lifestyle/home-garden/2021/02/23/gardening-you-winter-hardy-plants-made-through-no-damage/<personal data hidden>/

Like some of the plants that didn't fare well in the Texas cold, paw paw trees are not well adapted to Minnesota growing conditions.  This includes winter temperatures as well as day length and other factors.

Although plants rated hardy to Zone 5, including paw paws, are sometimes grown in Minnesota, they are usually short lived and subject to winter damage.  Reportedly, if/when paw paw fruit develops it may not ripen properly.

If you try to grow paw paws here, choose a sheltered location and select stock produced in the northern part of its range--Michigan, northern Indiana, Illinois and southern Wisconsin.

The following note and publications may be of interest:

https://ask2.extension.org/kb/faq.php?id=679502

https://ag.purdue.edu/hla/pubs/HO/HO-220.pdf

https://www.canr.msu.edu/news/winter_tests_limits_of_plant_cold_hardiness