Hi , You need to separate print size from aspect ratio. When you crop an image in Lightroom, you are cropping to an aspect ratio. when an image is printed , you select a paper size and fill or over fill that paper. In lightroom , on the crop tool , look for ‘Aspect Ratio’ Open the drop down menu and select 4×5/8×10. This aspect ratio will give you the exact same image, just on different size paper. Now crop your image. I am going to assume your are printing from Lightroom. when you go to print. Set up the printer for the size paper you have. You should also understand that most printers will not print 100% borderless. I always use larger paper and trim the image down after printing, prevents other set of problems. In the print module select an 8×10 template and load your image. Now it should print exactly what you crop.
Contact me at firstname.lastname@example.org if you need any other assistance.