I recently got 2 fat (1001) Sony PSP consoles, one with 3.71 M33 and the other with 3.51 firmware installed. Once I realized I cannot play ISO/CSO images from 3.51, I decided I want to upgrade to more recent firmware version.
Well, this turned out to be quite a trip since 3.51 first needs to be downgraded to 1.50 and then upgraded to 3.52, which then had to be upgraded to 3.52-M33-3 from which I could actually move up to 5.00-M33-6. Peace of cake 
This post helped me find out how to create a "magic" memory stick (though I used newer version of PSP Pandora Deluxe) and pandora battery (luckily I've had 2 fat PSPs of which one was already 'customized'), downgrade to firmware 1.50 and restore pandora battery back to a normal one. Once on 1.50, it was pretty easy to follow "regular" update process.
Having done 3.51 to 5.00-M33-6, I realized it would be nice to have the 3.71 upgraded as well, so I tried direct upgrade and found myself locked into a nasty EEEEEEEF update error not being able to boot PSP up at all. This is where "magic" memory stick saved the day and downgraded (semi-?) bricked PSP to 1.50. From that point on the upgrade process was the same as for the first PSP.
Was it worth $20 paying someone else do it? Maybe. Was it fun? Hell yes! 