Plus Primes vs Minus Primes
05AB1E, 10 9 bytes

Saved 1 byte thanks to Erik the Outgolfer

Outputs as [PlusPrimes, MinusPrimes]  

LDpÏ6%5Ñ¢


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Explanation

L             # push range [1 ... input]
 DpÏ          # keep only primes
    6%        # mod each by 6
      5Ñ      # divisors of 5 [1, 5]
        ¢     # count