According to Wilson's theorem if $p$ is a prime number we have $p\mid (p-1)!+1$ so if we prove that for infinitely many prime numbers $p$, $(p-1)!-1$ is composite we're done.
Since $p-1=-1 \pmod p$ and $(p-1)!=-1\pmod p$ we can conclude that $(p-2)!=1\pmod p$ so if we prove that for infinitely many prime numbers $p$,$(p-2)!+1$ is composite we're also done.
So if we consider that for sufficiently large prime numbers $p$, both $(p-1)!-1$ and $(p-2)!+1$ are prime numbers and have a contradiction with this suppose the problem is solved.