Help with Inequality with Exponents question

magic_castle32
How do you prove the following?

$$7^{\sqrt{5}} > 5^{\sqrt{7}}$$

Without calculators or working out $${\sqrt{5}}$$, $${\sqrt{7}}$$, of course.

$$7^5 \ and \ 5^{\sqrt{35}}$$
$$6 = \sqrt{36} > \sqrt{35}$$