I'm feeling quite stupid at the moment. The direct product $\,\Bbb Z/5\Bbb Z\times\Bbb Z/5\Bbb Z\,$ should have order 25, right?
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If by Z/Z5 you mean $\Bbb Z/5\Bbb Z$, then yes, you are correct. Any time we use a direct product $A\times B$, there will be $|A|\cdot |B|$ elements.