I also have the N5110 and recently upgraded to Windows 10 Home Edition (64 bit). I had the black screen issue as well, and finally figured out it was defaulting to an extended display. I plugged into my TV and was finally able to see that Windows had installed properly. I deleted the HD Intel drivers, and it defaulted to a Microsoft driver. This made my built in laptop display work, but the resolution kept defaulting to 1024 x 768, which is not the native resolution.
I found another thread in the Dell community on this same issue, and followed the advice of trying to update my BIOS version first. I updated it to the latest available, and then updated the drivers for the HD 3000 Intel Graphics Driver, and everything is back to normal. My built in display is outputting at the native resolution of 1366 x 768, and it is looking and running great. I hope this helps others who run into this same issue.