Answer
$ 2\sqrt {29}$
Work Step by Step
To find the distance between $(1,-3)$ and $(5,7)$,
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: $d=\sqrt {(5-1)^{2}+(7-(-3))^{2}}$.
We then simplify to arrive at the answer: $d=\sqrt {4^{2}+10^{2}}=\sqrt {116} = 2\sqrt {29}$.