Answer
See below
Work Step by Step
Given: $B=70$ degrees
$a=5$
Thus, $C=90$
It is a right triangle. Hence, the sum of two non-right angles of a triangle is 90 degrees:
$B=90-A=90-70=20$ degrees
We know $\tan B=\frac{b}{a}\\
\rightarrow b=a\tan B=5\times \tan 70\approx 13.74$
Apply the Pythagorean theorem to find c:
$a^2+b^2=c^2\\c=\sqrt a^2+b^2\\c=\sqrt 5^2+(5\tan70)^2\approx14.62$