Incorrect. Rationalize the denominator by multiplying the numerator and denominator by the denominator's conjugate:

$\displaystyle\frac{{{\left(\sqrt{{{5}}}+\sqrt{{{7}}}\right)}}}{{{\left(\sqrt{{{6}}}-\sqrt{{{5}}}\right)}}}\cdot\frac{{{\left(\sqrt{{{6}}}+\sqrt{{{5}}}\right)}}}{{{\left(\sqrt{{{6}}}+\sqrt{{{5}}}\right)}}}\usepackage{cmbright}\Huge\$

Use FOIL and then simplify the radicals.