Will this camera meet the requirements for my class?

Http://www.bestbuy.com/site/Nikon+D5000+12.3M+Digital+SLR+Camera%2C+Red+Backpack%2C+Battery%2C+Extra+55-200mm+Lens/9999160300050020.p?id=pcmprd160200050020&skuId=9999160300050020&st=Nikon%20D5000&lp=2&cp=1

Nikon D5000 12.3M Digital SLR Camera, Red Backpack, Battery, Extra 55-200mm Lens

Prerequisite: Students are required to provide a 35mm Digital SLR camera and lens with adjustable shutter and aperture with lens and memory card. The camera must be a eight megapixels or higher. Students are required to provide their own printing paper, CD-R s, DVD-R s, Jump Drives, or Portable Hard Drives with fire wire capability. Students may need an extra battery for your camera. The College provides all other lab equipment, supplies and use of a modern photo and digital labs.

Probably yes, except for the 35mm part. That's a crop frame DSLR, not a full frame (35mm) one.

I do think that this may be a typo or copying error from another list that was about film SLRs though (which are called 35mm SLRs as 35mm is the diameter of the film frame). That's because there's little reason to demand that students bring a full frame DSLR, and full frame ones start at about $2500 - without a lens, that is.

So… I think you should ask them to clarify that requirement, as it most likely has a mistake in it. If they don't insist on the 35mm part, then that camera would suit the requirements. I'm not terribly fond of those bundled offers though, as you might not put that second lens to much use if it doesn't suit your preferences. Note that the D5000 meanwhile has been superceded by the D5100.
I'd get a D3100 or D5100 or D90 with just the basic kit lens instead.

Edit: A thumb down? Well, if i'm mistaken about something, just step forward and correct me.

Since there are NO 35 mm digital cameras. 35 mm cameras use film. Digital cameras use a sensor instead, you need to get some clarification from your school.

The D5000 is an excellent camera if you really just need a fine dSLR

Definitely clarify. There are some better photography programs that do not allow the use of the entry level DSLR's and it really may be that it requires a full frame. I haven't run into one that requires full frame, but that doesn't mean anything.
It is PROBABLY perfectly fine. My guess would be that the course description is written by someone who is confusing the 35mm as any DSLR.