To find side $ a $ use Law of Cosines:
$$ a^2 = b^2 + c^2 - 2 \cdot b \cdot c \cdot \cos( \alpha ) $$After substituting $b = 7$, $c = 5$ and $\alpha = 65^o$ we have:
$$ a^2 = 7^2 + 5^2 - 2 \cdot 7 \cdot 5 \cdot \cos( 65^o ) $$ $$ a^2 = 49 + 25 - 2 \cdot 7 \cdot 5 \cdot \cos( 65^o ) $$ $$ a^2 = 74 - 2 \cdot 35 \cdot \cos( 65^o ) $$ $$ a^2 = 74 - 70 \cdot 0.4226 $$ $$ a^2 = 74 - 29.5833 $$ $$ a^2 = 44.4167 $$ $$ a = \sqrt{ 44.4167 } $$$$ a \approx 6.6646 $$