Help with building a NFA automaton
Just a hint:

If the requirement was to count the length $3n$, the NFA was simple, and could be done with 3 states. Similarly, if you only needed the $5m$ part, an easy 5-state NFA could do this.

Now think how to "combine" these two NFAs, one on top of the other. Use $\epsilon$-moves to go from the end of one, to the start of the another. Because you need $|Q|=5$, you will have to overload the meaning of 3 states so they serve both the $3n$ and the $5m$ machines.

Another hint that may be helpful: make $q_0$ accepting (and the only accepting state).

Good Luck.