I noticed that for a wide range of $m > 55$, the result of
$$ 2^2 \cdot 3^2 \cdot 7^m$$
always contains a $5$.
Is there a known reason for this? Or is there a counter-example?
Note $\mathit 1$: I only tested this for $m \leq 50,000$
Note $\mathit 2$: There seems to be a similar pattern for $2^{2} \cdot 3^{2} \cdot 11^{m}$ (starting at $m=43$) and $2^{2} \cdot 3^{2} \cdot 13^{m}$ (starting at $m=34$)
Note $\mathit 3$: Similar for $7^{m}$ (for $m > 25$; tested for $25 < m < 75,000$)