best way is to upgrade to 2.71 then back to 1.5 then goto 3.10oe-a from there.
stuff needed :
1:
sony 2.71 usa update
2:
2.71 to 1.5 downgrader (non ta-o82)
3:
3.10oe-a installer (get the installer for 1.5 user's)
this is how i always do mine and i confirm they work great.
to upgrade to 2.71:
1: download the 2.71 sony update eboot.
2. Plug in your PSP to your computer using a USB cable.
3. Select USB Connection from the 'settings' menu in the XMB
4. Open the Drive letter your computer assigns to your PSP (e.g E:\)
5. Open the "PSP" folder, then open the "GAME" folder.
6. Make a folder called "UPDATE" and make sure it is in caps.
7. Copy the firmware update into your "UPDATE" folder on your PSP.
8. Make sure the firmware update file is called "EBOOT.PBP"
9. Close the USB Connection and disconnect your PSP from your computer.
10. Make sure you have a full battery or plug in your PSP into the AC Adaptor.
11. Go to the memory stick under "Game" on your PSP and you should see the PSP firmware update.
12. Highlight the firmware update and press 'start' to start the update.
13. Now follow the on-screen instructions.
14. Once the update has finished, restart your PSP.
15. Now go to Settings > System Settings > System Information and check that the System Software has been updated.
Now you have successfully upgraded your PSP firmware.
===========to downgrade from 2.71 (non ta-082)===========
1. Format your memory stick using your PSP.
2. Unzip the Update Flasher Package to a folder on your computer.
3. Copy all contents inside the MS_ROOT folder to your memory stick.
4. Go to the PHOTO viewer of the XMB and enter in the folder "HENC".
- If your PSP freezes, restart your PSP and try again.
- A blue screen will appear the first time you run this program and after that you'll either see:
Red: The files couldn't be written to the flash, keep trying.
Green: The files were written successfully. The PSP will reboot shortly.
You can now run the downgrader included in the package.
5. Run the downgrader by running it from "Game > Memory Stick".
6. The rest of the steps are pretty simple, follow the on-screen instructions.
7. Format your memory stick after you've finished the downgrade.
theres a read me with the 3.10oe-a installer and i know you have done them before so it should be a piece of cake for you