There are 5d monic polynomials of degree d over F5. For each degree, the number of monic irreducible polynomials over F5 is given by A001692 in the OEIS. Numbers of primitive polynomials are given by A027741.
Bosma, W.; Steel, A. "Magma handbook: finite fields". Computational Algebra Group, School of Mathematics and Statistics, University of Sydney. Retrieved 29 November 2023.