Proof of set is a subset of another set?

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Prove      {5^(6n+2) : n ∈ Z} ⊆ {125^m/5 : m ∈ Z}

I have worked out doesn't look correct?

I have done it by taking 125^m/5   ->  5^(6n+2)/5 
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Hint:

$$5^{6n+2}=5^{6n+3-1}=\frac{5^{3(2n+1)}}{5}$$