Which is better-A telescope or a telephoto zoom lens?

Which could be better for my Nikon D5100-a telescope or a telescope zoom lens? And why?

What are you wanting to take photos of? The moon? No such thing as a " telescope zoom lens". There's a telephoto lens… Which is good for taking photos of things at a distance.

"Better" for what?

For sports or birds or wildlife, a telephoto zoom lens would be "better."
For the moon, planets, stars, galaxies, nebulae -- a telescope would be "better."
But unless you've got the right kind of mount for the telescope (specifically a motorized equatorial mount that tracks contrary to the rotation of the earth), you're not going to do very well with a telescope…

Ditto on "Better" for what?

No way to answer unless you say "what"

Telescopes usually offer longer focal lengths but they do not have an adjustable aperture, and they usually have a slow aperture.

Telescopes are only designed to focus on infinity and will give poor results if you focus closer.

Most telescopes are also designed only to project an image into your retina, not onto your camera sensor. They will usually suffer from aberrations not present in camera lenses.

Telescopes are bigger and heavier, and lack autofocus.

If you are wanting to do astronomy then get a telescope. For everything else, get a telephoto lens which will have better glass, autofocus, faster aperture, smaller size, etc, etc.