Answer
$$ {x^{2}}-\dfrac {y^{2}}{25}=1$$
Work Step by Step
Equation of hyperbola with a format of
$$\dfrac {x^{2}}{a^{2}}-\dfrac {y^{2}}{b^{2}}=1\left( a > 0,b > 0\right) $$
Vertices are $\left( \pm a,0\right) $
Asymptotes are $y=\pm \dfrac {b}{a}x$
Given vertices $(\pm1,0)$ we find $a=1$ and given asymptotes $(\pm5x)$ we find $\dfrac{b}{a}=5$
$\Rightarrow b=5$
Then the equation will be
$$\Rightarrow {x^{2}}-\dfrac {y^{2}}{25}=1$$
