Are lenses from nikon d5100 compatible with nikon d800?

And what lenses are best for nikon d800?

Nikon D5100 is a APS-C based sensor camera and Nikon D800 is a Full Frame.

You can use FX lenses on Nikon D800, DX lenses are made for crop sensor camera like D3200, D5100 etc.

FX designated lenses would be best for d800 since it has a 35mm sensor. A DX camera such as d5100 has a smaller sensor. If you use a dx lens on d800, the camera would go into crop mode, you would see heavy vignetting and you wouldn't be able to use all of those 36mp you bought it for.

Yes.

Your D5100 can use either DX (cropped) or FX (full frame) lenses equally well. The D800 prefers to use FX lenses, but can use DX lenses in cropped mode.

So it depends on what lenses you have for your D5100 whether or not you should buy new ones for a D800.

For instance, should you have a Nikon AF-S 70-200mm f/2.8, there's no need to buy a new lens as it will work on the D800 just fine. But if you have a Nikon AF-S 55-200 DX, then you will want to upgrade that lens as it is a consumer-level cropped lens, and you want all pro-glass for a D800.