Answer
$A=40°$
$a\approx3.23$
$b\approx3.55$
Work Step by Step
First, we can calculate the third angle by the rule of:
$A+B+C=180^{\circ}$
Here, we have
$B=45°$
$C=95°$
Therefore
$A=180°-95°-45°=40°$
Now, by applying the Law of Sines we can calculate the remaining two sides:
$$\dfrac{\sin(A)}{a}=\dfrac{\sin(B)}{b}=\dfrac{\sin(C)}{c}$$
We know one side of the equation, which is:
$$\dfrac{\sin(C)}{c}=\dfrac{\sin(95°)}{5}$$
First, we calculate $a$:
$$\dfrac{\sin(A)}{a}=\dfrac{\sin(C)}{c}\\
\dfrac{\sin(40°)}{a}=\dfrac{\sin(95°)}{5}$$
Cross-multiply, then isolate $a$ to obtain:
$$a\cdot \sin95°=5\cdot\sin40°\\
a=\dfrac{5\cdot\sin40°}{\sin95°}\\
a\approx3.23$$
Next, solve for $b$:
$$\dfrac{\sin(B)}{b}=\dfrac{\sin(C)}{c}\\
\dfrac{\sin(45°)}{b}=\dfrac{\sin95°}{5}$$
Cross-multiply, then isolate $b$ to obtain:
$$b\cdot\sin95°=5\cdot\sin45°\\
b=\dfrac{5\cdot \sin45°}{\sin95°}\\
b\approx 3.55$$
