Answer
$5$
Work Step by Step
To find the distance between $(1,1)$ and $(4,5)$,
we use the distance formula: $d=\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$.
We plug in the given $x$ and $y$ values: $d=\sqrt {(4-1)^{2}+(5-1)^{2}}$.
We then simplify to arrive at the answer: $d=\sqrt {3^{2}+4^{2}}=\sqrt {25} = 5$.