Your friend is right that it is actually always a 24mm lens — that is a property of the optics and never changes. But, he's wrong in saying that the crop factor does not apply. That's a property of the sensor size of the camera.

From a practical point of view, zoom — changing focal length — and cropping are interchangeable. So, using a camera with a smaller sensor (a "cropped" sensor) is effectively like using a longer focal length in several important ways, the most important of which is the field of view.

If, using the same camera, you take a photo with a 24mm lens and a 36mm lens, but crop the center 2/3rds from the 24mm photo and blow it up to the same size as a print of the 36mm image, the two photos will look virtually identical. (The blown-up image will have little more blur, of course — that's why we have different focal length lenses instead of just cropping. And in the real world there will be other unavoidable differences.)

When you mount the 24mm lens on a film camera, it has a horizontal field of view of about 74°. When you mount it on the D5000, it still projects the same image, but you only get the center portion, because the sensor is only that big, leaving you with a field of view of about 53°. That's the crop factor.

See What is "angle of view" in photography? for more on this — my answer there has an illustration which explains how this works.

In any case, the net effect of this is thankfully simple: the focal length of any lens, ancient or brand new, is an inherent property of the lens. It doesn't matter when it was made or what camera it was made for. If a camera has a sensor smaller than 35mm film, the crop factor can be applied to get an idea of the focal length which would give the same view on that format. That factor is also non-magical: because the sensor size of a given camera doesn't change, the crop factor always applies no matter what lenses you attach.

Another answer mentioned the coverage of the image circle. This is the circle of light projected from the back of the lens, and it is true that lenses designed for smaller sensors sometimes don't cover a full-frame sensor. That lets them be smaller, lighter, and cheaper, but has nothing to do with crop factor.

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Note: the only times I've ever seen number printed on the lens or in specs "pre-converted" to 35mm-equivalent (by applying the crop factor to the real number) is on cameras with non-removable lenses. It's incredibly common in cameraphone specifications, and you'll often see it for superzoom compacts. That's probably mostly because the bigger numbers sound more exciting, not in an effort to be more useful. But I've never seen an interchangeable-lens system use anything but the real, physical numbers.