Q:

Show that $m=6k+5$ has at least one prime divisor of the form $6n+5$

What's the best way of approaching this kind of questions? 

A:

Imagine factoring $m$ into primes.
$m$ cannot have $2$ or $3$ as a factor (why?)
All other primes are equivalent to $1$ or $5 \pmod 6$
If you multiply together numbers equivalent to $1 \pmod 6 \dots$

