Hi there.
Assume 33k+2k+2=5A, ie 33k=5A-2k+2, where A is an integer
Prove for n=k+1, ie prove 3k+3+2k+3=5B, where B is an integer
LHS=3k+3+2k+3
=32(5A-2k+2)+2k+3 by the assumption
=5x27A-108x2k+8x2k
=5x27A-100x2k
=5(27A-20x2k)
=5B, where B=27A-20x2k
.: true for n=k+1
There you go.