#### Answer

The radius of the event horizon is 14.7 km

#### Work Step by Step

We can use the equation for escape speed to find the radius $R$ of the event horizon.
$v = \sqrt{\frac{2~G~M}{R}}$
$v^2 = \frac{2~G~M}{R}$
$R = \frac{2~G~M}{v^2}$
$R = \frac{(2)(6.67\times 10^{-11}~m^3/kg~s^2)(5.0)(1.99\times 10^{30}~kg)}{(3.00\times 10^8~m/s)^2}$
$R = 1.47\times 10^4~m$
$R = 14.7~km$
The radius of the event horizon is 14.7 km