Yes, you can use CD with the Alt+F2 (EZ Flash 2).
Bear in mind that the new downloaded BIOS should have the same name as the BIOS that the board shipped with when making the CD image- so check your mobo support disc ( the one with the drivers and utilities on it). In fact, you could use that disc as the EZ Flash utility should look for the appropriate .ROM BIOS file - although it might be an older BIOS version.
I quickly checked the Asus site. The newest BIOS is named P5E3-1503.ROM -so just rename to whatever the mobo support dvd BIOS is ( Browse the DVD root directory and you should happen across the P5E3.ROM (or similar) BIOS.
I'm assuming (possibly wrongly) that you have already cleared CMOS via the jumper as well as using the CMOS button. If you have not, then I would strongly advise that you do this before reflashing just in case the CMOS button isn't doing it's job- there should be a small 3-pin jumper (CLRTC) just above the front panel connectors on the mobo (somewhere in the bottom right-hand corner). Check your mobo manual under "Jumpers" - but basically:
>Turn off the computer, unplug from the wall outlet, hit the power button a few times to discharge any residual charge
>Move the jumper cap from pins 1 & 2 across to 2 & 3. Leave for a short time -half a minute or so.
> Move the jumper back to pins 1 & 2
> Power up > hit Delete during POST to enter BIOS