AF motor not working in viewfinder but works in live view?

Hi! I have a Canon 60d and I realized that the AF motor might have issues. I'm not quite sure what the issue is. I can use the 18-55 lens with no problem. But when I try using a 50mm f1.8 or a 35mm f2 the AF doesn't seem to work in the viewfinder. It just makes slight tweak sounds like its trying to focus but it can't. Weird thing is that when I switch to live view the AF works for the 50mm and the 35mm lens. This left me to wonder that maybe the lens might have an error. I tried using the 50mm and 35mm lens on my Canon T5 and it seems to work perfectly. So I'm not sure if there just an in compatibility with the prime lens with the 60d because they are EF lens made for full frame. I'm not sure if the 60d doesn't function with full frame lens. My T5 is a crop sensor and it works with them so I'm very confused about what the issue is. Help me out thx!