Answer
$77-31\sqrt{7}$
Work Step by Step
Use the FOIL method, with
$\sqrt{a^{2}}=(\sqrt{a})^{2}=a$ (for positive a).
$F:\quad 7\times 5=35$
$O:\quad 7\times(-3\sqrt{7})=-21\sqrt{7}$
$I:\quad -2\sqrt{7}\times 5=-10\sqrt{7}$
$L:\quad -2\sqrt{7}\times(-3\sqrt{7})=+6(\sqrt{7})^{2}=6\times 7=42$
Add like terms: (F+L)+(O+I)
$...$= $77-31\sqrt{7}$