The language L = {G | G has a clique in size of n-5 and has no IS in size of n\2}

as n = |V|.

The solution says that the smallest class L is in - is P. That's because for a big enough n, if there's a clique in size of n-5 there's definately no IS in size of n\2. We only need to check if there's a clique in size n-5 and that happens in poly time.

What I don't understand is why it's P and not NP. Sure, checking if a subset of V is a clique in size of n-5 takes poly-time but we need to have multiple checks, for different options of subsets in size of n-5, and accept if one is valid (if the subset is a clique). Isn't that NP?