Would google apps for a lower android version work for the higher one? I'm trying to install a custom Rom of android version 6.x. But I installed the google apps for version 5.x. 
Would they work fine if I install them together?
Yes, Google Apps for older Android versions still work with the latest version of Android (usually, with Android 6 they need a fix to give them some permissions)

Although they might work, I recommend getting OpenGApps for your Android version for better compatibility and the latest patches.