Nikon sb-80dx speedlight on a Nikon D5000?

I'm using a sb-80dx on my D5000 and it works great. It is TTL not i-TTl and I don't know what features or difference it is?
Why does it only let me use M mode on the camera and not A, S, P? When I use those the camera chooses a really slow shutter speed. I have to shoot in M and use my knowledge for the exposure settings. I think the camera doesn't communicate with the flash right. Also the recycle time takes forever sometimes! How can I make it faster? I'm using Duracell and energizer AA, I heard rechargable batteries will give faster recycle times? Do I need a flash diffuser, or is the built in bounce card good?

Added (1). The manual for the the sb-80dx only goes up to page 105. The slow recycle time is the worst problem I'm having, I think I'm going to get a sb-600. Still don't know why it's still so slow.

Look on page 200 of your user manual. From what I read, the SB-80DX should work in all modes

Faster recycle (and shorter flash duration, nice when shooting things like splashing water) is accomplished by using the flash at 1/4 to 1/16th power

That flash uses an older Nikon TTL system called D-TTL, which was last used on the D100 body. Your camera uses i-TTL, which is an entirely different system and not compatible. That is why the flash doesn't talk to the camera in TTL mode.

Put the flash in manual mode, where you set the flash power yourself, or I believe it has an Auto mode that should work better with your camera as well.

The SB-80 shouldn't have a slow recycle, as it was the high-end of the Nikon flash line at one time. Fresh batteries should solve the problem, if not, then it may need service anyway.