Consider the linear congruence $15x ≡ b \pmod {25}$. Find the integers $b$ for which this linear congruence has solutions.
How many incongruent solutions does it have?
For there to be solutions $g=\gcd(25,15)=5$ needs to divide $b$.
So $b=5k$ for some integer $k$ means the linear congruence has solutions, and the number of incongruent solutions is 5.