If $5x \equiv 15 \pmod{25}$, then definitely $x \equiv 3 \pmod{25}$. Is this true or false? I don't understand how to prove this statement true or false.

If $5x \equiv 15 \pmod{25}$, then definitely $x \equiv 3 \pmod{25}$.  

All I know is that $\frac{5}5x \equiv \frac{15}5 \pmod{\frac{25}5}$ = $x \equiv 3 \pmod{5}$, and $x \cdot 5 \equiv 3 \cdot 5 \pmod{25}$ = $5x \equiv 15 \pmod{25}$, how do you prove this equation? 

The congruence $5x \equiv 15 \pmod{25}$ means that there exists $t \in \mathbb{Z}$ such that 
$$5x = 15 + 25t$$
Dividing each side of the equation by $5$ yields
$$x = 3 + 5t$$
Therefore, if 
$$x \equiv 3 \pmod{5}$$
it satisfies the congruence $5x \equiv 15 \pmod{25}$.  There are five such equivalence classes modulo $25$.  They are 
\begin{align*}
x & \equiv 3 \pmod{25}\\
x & \equiv 8 \pmod{25}\\
x & \equiv 13 \pmod{25}\\
x & \equiv 18 \pmod{25}\\
x & \equiv 23 \pmod{25}
\end{align*}
Hence, the statement is false.
