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?

$$
6^{k+1}-{5}^{k+1} = (6-5)(6^k + \cdots + 5^k) = 6^k + \cdots + 5^k \ge 6^k + 5^k \ge 6+5 =11 > 9
$$
for $k\ge 1$.
