The distance between points $ A $ and $ B $ is :
$$ d(A, B) = 5 $$To find distance between points $ A(x_1,y_1)$ and $ B(x_2,y_2)$, we use formula:
$$ \color{blue}{ d(A,B) = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} } $$In this example we have:
$$ \begin{aligned} & A \left(5,~2\right) \implies x_1 = 5 ~~\text{and}~~ y_1 = 2 \\[1 em] & B \left(2,~-2\right) \implies x_2 = 2 ~~\text{and}~~ y_2 = -2 \end{aligned} $$Substituting $ x_1 $, $ x_2 $, $ y_1 $ and $ y_2 $ into the formula above yields:
$$ \begin{aligned} d(A,B) & = \sqrt{\left( 2 - 5 \right)^2 + \left( -2 - 2 \right)^2} \\[1 em] d(A,B) & = \sqrt{ (-3)^2 + (-4)^2 } \\[1 em] d(A,B) & = \sqrt{ 9 + 16 } \\[1 em] d(A,B) & = \sqrt{ 25 } \\[1 em] d(A,B) & = 5 \end{aligned} $$