Automorphic Numbers with 5 Digits

Theorem
The only $5$-digit automorphic number which does not begin with a zero is $90 \, 625$.

Proof
We have:
 * $90 \, 625^2 = 8 \, 212 \, 8 \mathbf{90 \, 625}$

thus demonstrating it is automorphic.