Inductive step: Assume that $5^{k}<5^{k+1}$ for some positive integer $k.$ We want to show that $5^{k+1}<5^{k+2}.$
Starting with $5^{k+1},$ we can rewrite it as $5^{k}\cdot5.$ Using our assumption, we know that $5^{k}<5^{k+1},$ so we can substitute that in to
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