Stating the obvious, but 5 is just 4+1. It's called odd time because it is based on an odd number, but there is nothing odd about it. Overthinking it will create more obstacles. Get rid of the notion of it being odd, strange, etc. In some parts of the world 5/4 is common time.
Definitely agree with mrfingers. Create a playlist of songs in 5, and listen to them ALOT. A few songs were already mentioned. Two more I am sure you know... the theme from Mision Impossible, and Take Five by Dave Brubeck. Some of my favorites... Seven Days by Sting, English Roundabout by XTC, and WTF? by OK Go.
For rudiments and fills, doing some work on a pad won't hurt.
Use a metronome, and count out loud.
Start with 5 stroke singles accenting the 1 (downbeat). Do the same accenting the 3, and then the 4. The latter are the most common place for the backbeat in 5/4. After singles, work on 5 stroke stickings with doubles: para-pa-diddle (rlrll and lrlrr); para-diddle-pa (rlrrl and lrllr); pa-diddle-diddle (rllrr and lrrll); and diddle-pa-diddle (rrlrr and llrll). Transfer that to the kit, and work on orchestration.
Again, don't overthink it. Have fun!

