I purchased a psp slim today and it has firmware 4.05, what do I need to do to get it to run homebrew and (legal) roms?

Ask Wilhelm.

To run anything homebrew you need to downgrade your psp. For some reason the older firmware allowed homebrew apps and such, for as the more recent firmware would not. note: Downgrading is considered illegal at the point where you start running software that isn’t original PSP software. It is reversible, but when you brick* your PSP. Your warranty doesn’t cover it.
*your psp hung up during installing older firmware and is as good as a brick
Read all instructions carefully, you can start at this Wiki-how article. It’s wise to read as much as you can on this subject on various websites before trying this.

p.s. Sony now provides various GUI skins for free on their PSP website.

i Would not try to downgrade your psp slim as the motherboard was not made to run older firmwares. the best solution is to install a custom firmware.
This article tells you how to downgrade the slim. QJ.net and PSP3D is great sites and forums for psp talk. (I’m active at psp3d, my name is wilhel1812)

@Jax downgrading is not in any way illegal! Trust me, i know.

it’s not the downgrading but the point where you start running non native software. Not that sony would know you are. It’s safer to say they don’t apriciate it and use it to blame defects on the user.

Still not illegal unless you run software that is pirated. And that has nothing to do with sony, but the ones that made the software you pirated. I’ve been making homebrew games myself, and this is not illegal.

Try half byte loader. I did for my PSP Slim cfw 6.20 and it works great.