Showing that $\{ c^n a^m b^{n+m} : n+m \geq 6\}$ is not regular

Question

I'm trying to show that $L_6=\{c^n a^m b^p : n+m=p,p \geq 6\}$ is not regular. I need a little help, I was practicing the pumping lemma, and I encountered this language, I saw these conditions and got totally confused, what to do now?

Earlier I showed that $L_5=\{a^n b^n : n≥0\}$ is not regular. In this Language it was very simple to choose $w$, namely $w= a^pb^p$, where $p$ is the pumping length. But this new Language is complicated, so I thought you guys could help me out.

Answer 1

If $L_6$ were regular, then so would the following language be: $$ (L_6 \cap a^* b^*) \cup \{ \epsilon, ab, a^2b^2, a^3b^3, a^4b^4, a^5b^5 \}. $$ However, this language is none other than $L_5$.

You can also use the pumping lemma. Try to pump the word $c^qa^qb^{2q}$ for large enough $q$.