Can I further simplify $5^k \cdot 5 + 9 < 6^k \cdot 6$ to prove this is true I am trying to prove this statement, but I'm not sure where to go from here.  Is don't think this is sufficiently reduced to conclude the statement is true, but I'm not positive.
$k ≥ 2$
Can I further simplify this?

You can prove it by induction suppose $5^{k+1} + 9 < 6^{k+1}$ that this is correct and you should prove it for $k+1$ so using the induction assumption the left side is smaller so what it would be if you multiply the part of left side by another $5$ and the right side by another $6$? the left side will be still smaller?
