Quick answer

$5n$ ends with digit $0$ if and only if $n$ is even.

So the statement is not true for every natural number. It is true exactly for even $n$ (and also for $n=0$ if your convention includes 0 in naturals).

Why

A number ends in $0$ exactly when it is divisible by $10$.

So we need: $$ 10 \mid 5n. $$ Since $10 = 2 \cdot 5$, this means $5n$ must have a factor $2$. The factor $5$ is already present, so this happens exactly when $n$ is even.

Quick check

$n$ $5n$ Last digit
1 5 5
2 10 0
7 35 5
12 60 0

Visual pattern

Odd n gives last digit 5; even n gives last digit 0.

Therefore, $5n$ can end with $0$, but only when $n$ is even.