|No reason was ever given as to why the Fifth Doctor was wearing a cricket uniform.|
He only played cricket once.
I tried to find this video from the "Castrovalva" DVD (Davison's first episode) which had this great video featurette called "The Crowded TARDIS" which showed one of Peter Davison's first interviews after being cast as the Doctor and you wouldn't believe how unimpressed he looked at the prospect of being the Doctor. I couldn't believe it! How could you not be excited about being the Doctor?
But his performance didn't reflect the same apathy.
The Fifth Doctor era was meant to be more of a back to basics era. The sonic screwdriver was retired as part of the show's attempt to get away from both horror and humor in favor of more scientifically based stories.
|Science and realism. That's what the 5th Doctor era was really about.|
|"I'm the Doctor, I can save the universe using a kettle and some string, and look at me, I'm wearing a vegetable"|
Yet, Davison's Doctor was much more serious than his predecessor. Tom Baker's Doctor very rarely stopped joking around. He was always quick with a quip, no matter how seemingly dire the situation. Davison's Doctor could see the severity of dangerous situations, and could mourn for the first (and, thus far, only) companion to actually die on the Doctor's watch. It was a truly sad and dark moment that couldn't have been handled with the appropriate weight even by Tom Baker (even though, as you've probably already realized, he's higher on my list than Davison).
In 2007, Moffat wrote the brilliant mini-episode, "Time Crash," which, despite being only a few minutes long, was the first multi-Doctor episode of the revived series, and made Peter Davison into the first (and, it looks like, only) classic series Doctor to appear in the new series. Let's use the words of Moffat, the master writer himself, to explain why Peter Davison was so utterly awesome: