Michael, you are in luck as the screen in the Asus R500V is pretty easy to replace, but unfortunately I don't see any similar laptops on this site with screen replacement guides so I'll try to walk you through.
1. Remove the two Phillips head screws at both bottom corners of the screen, covered by little rubber feet.
2. Pry off the front bezel, starting from the middle bottom of screen where the bezel covers the metal part of the screen and working your way out and up.
3. Remove all the screen that hold the hinges to the back panel near the base of the screen.
4. Disconnect the LCD cable.
5. Remove the Phillips head screws on both sides of the screen to pull it off of the hinges.
My recommendation is that you order the screen based on the part number on the screen itself. $50-60 is pretty normal for a 15.6" screen, and the $119 for a screen replacement is not a bad deal if that includes the screen and labor.