Answer
$$d = \sqrt {56} $$
Work Step by Step
$$\eqalign{
& {\text{Let the points be }}\underbrace {\left( { - 2,1, - 5} \right)}_{\left( {{x_1},{y_1},{z_1}} \right)},\underbrace {\left( {4, - 1, - 1} \right)}_{\left( {{x_2},{y_2},{z_2}} \right)} \cr
& {\text{Finding the Distance Between Two Points}} \cr
& d = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2} + {{\left( {{z_2} - {z_1}} \right)}^2}} \cr
& d = \sqrt {{{\left( {4 + 2} \right)}^2} + {{\left( { - 1 - 1} \right)}^2} + {{\left( { - 1 + 5} \right)}^2}} \cr
& {\text{Simplifying}} \cr
& d = \sqrt {36 + 4 + 16} \cr
& d = \sqrt {56} \cr} $$
