Which affordable lens for zooming is best for a Nikon D5100?

Please people who own one and knows about this answer, thanks.

Stick with the 18-55mm until you can work it out for yourself.

What do you think is affordable?

If you want a longer zoom than the standard 18-55mm there's the 55-200 mm VR or the 55-300 mm VR if you want to go longer. Both are reasonably priced. The 55-200mm VR can often be picked up very cheaply and there are quite a few good secondhand ones around.

If you want ultrawide for sweeping landscapes consider a secondhand 10-20mm Sigma lens - but make sure you get the HSM version which will autofocus with your Nikon.

What do you mean by affordable?

One of the best general purpose lenses is the 18-200mm, but it may be beyond your budget.

Perhaps the two most popular telephoto lenses for your camera are the Nikon AF-S 55-200mm and the Nikon AF-S 55-300mm.