The distance between the line and the point is:
$$ d = \frac{ 7 \sqrt{ 10}}{ 10 } $$The distance from the point $ (x_0, y_0) $ to the line $ Ax + By + C = 0 $ is given by:
$$ d = \frac{ \left| Ax_0 + B_yo + C \right| }{ \sqrt{A^2 + B^2}} $$After substituting: $ A = 1 $ , $ B = 3 $ , $ C = -4 $ , $ x_0 = -4 $ and $ y_0 = 5 $ we have:
$$ \begin{aligned} d =& \frac{ \left| 1\cdot\left(-4\right) +3\cdot5 + \left( -4\right) \right| }{\sqrt{ 1^2 + 3^2}} = \\ d =& \frac{ \left| -4 + 15 -4 \right| }{\sqrt{ 1 + 9}} = \\ d =& \frac{ \left| 7 \right| }{\sqrt{ 10}} = \\ d =& \frac{ 7 }{ \sqrt{ 10 } } = \\ d =& \frac{ 7 \sqrt{ 10}}{ 10 } \end{aligned} $$