I recently bought a new focus screen for my D5100. I installed it without any problems. But, if I manually focus with the screen it is not correct. A picture of something 30ft away is about a foot off. The auto focus still works fine, but did I do something wrong with the focus screen?
You'll need to calibrate the positioning of your focusing screen. Usually, there are small rectangular shims which get the screen into exactly the right position. You may need to adjust these. Depending on where you bought the screen, it may have come with some. (Some cameras include shims to position the factory-installed screen, but some don't; I'm not sure of the case with the D5100.)