We have,

2x+3y=17k

Let us find all solutions for a given k>0.

This is a linear diophantine equations with two variables.

We see that,

2(-1)+3(1)=1

Thus,

2(-17k)+3(17k)=17k

Thus, all solutions are,

x=-17k+3t

y=17k-2t

For some integer t.

Thus,

9x+5y is,

9(-17k+3t)+5(17k-2t)=-153k+27t+85k-10t

Combine,

-68k-17t=17(-4-t)