The distance between points $ A $ and $ B $ is :
$$ d(A, B) = \frac{ 5 }{ 2 } $$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:
$$ \begin{aligned} & A \left(\dfrac{ 3 }{ 2 },~3\right) \implies x_1 = \frac{ 3 }{ 2 } ~~\text{and}~~ y_1 = 3 \\[1 em] & B \left(3,~5\right) \implies x_2 = 3 ~~\text{and}~~ y_2 = 5 \end{aligned} $$Substituting $ x_1 $, $ x_2 $, $ y_1 $ and $ y_2 $ into the formula above yields:
$$ \begin{aligned} d(A,B) & = \sqrt{\left( 3 - \frac{ 3 }{ 2 } \right)^2 + \left( 5 - 3 \right)^2} \\[1 em] d(A,B) & = \sqrt{ \left(\frac{ 3 }{ 2 }\right)^2 + 2^2 } \\[1 em] d(A,B) & = \sqrt{ \frac{ 9 }{ 4 } + 4 } \\[1 em] d(A,B) & = \sqrt{ \frac{ 25 }{ 4 } } \\[1 em] d(A,B) & = \frac{ 5 }{ 2 } \end{aligned} $$