Using newer Nikon lenses on older film SLRs?

So I'm a bit of the wrong way round here, compared to what most people ask. Haha.

I'm looking at buying a (cheap) 35mm Nikon SLR to have a play with and get to learn how to use film more. Having been interested in photography for a good few years now I've grown a little collection of lenses used with my newer Nikon D5000 DSLR.

My question being, can I use my AF-S lenses used with my DSLR with an older SLR, or will I need to invest a little more money for an older lens that wouldn't then be fully compatible with my DSLR?

I depends. If the older 35 mm SLR can use an auto-focus lens, there's no problem.

I use all my Nikkor AF and AF-S lenses on my old Nikon F4 (circa 1988)

If any of your lenses are "DX", then you will get some vignetting, but they will NOT damage the camera. It is only Canon EF-S lenses (Canon's version of the Nikon DX) will damage full frame cameras mirrors.

Why bother, you'll probably find all the MF lenses you'd ever want for a song.

Some of the older film cameras would not work with the G lenses, and your kit lens for the D5000 is a G lens. The G lenses have no mechanical aperture control ring, and so they need to be able to electronically interact with the camera body to set the aperture.
AF-D lenses normally have an aperture ring. Setting the ring to the highest f number tells them to be able to work electronically. So those would work with your digital SLR and a mechanical film SLR. One little catch is that these require a body with an autofocus motor to autofocus. Your D5000 lacks that.