That depends. If you can find drivers for Windows 7 (32-bit or 64-bit, depending on what version you buy - Windows 7 isn't free) on asus.com, it should work.
Same for Windows 10 (which is free, so you don't need to buy it, you can just download it.
Note that both Windows 8 and Windows 10 are supported by Microsoft. Windows isn't any longer. Why do you want to switch to an unsupported OS?
I have an Asus Vivobook V500CA-BB31T laptop
Windows 8 has been installed on the laptop since the purchase, can Windows 7 be installed on it, is it very difficult, and are there any problems?