Answer:
[tex]C=25^{\circ},\\a\approx 10.72,\\b\approx 11.83[/tex]
Step-by-step explanation:
The sum of the interior angles of a triangle is 180 degrees. Thus, angle C must be [tex]180-90-65=25^{\circ}[/tex].
In any triangle, the Law of Sines is given by [tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex].
Therefore, we have:
[tex]\frac{\sin 90^{\circ}}{b}=\frac{\sin 25^{\circ}}{5},\\\\b=\frac{5\sin90^{\circ}}{\sin 25^{\circ}}=11.8310079158\approx \boxed{11.83}[/tex]
[tex]\frac{a}{\sin 65^{\circ}}=\frac{5}{\sin25^{\circ}},\\a=\frac{5\sin 65^{\circ}}{\sin25^{\circ}}=10.7225346025\approx \boxed{10.72}[/tex]
