#### Answer

$x=\pm\dfrac{\sqrt{35}}{5}$

#### Work Step by Step

Using the properties of equality, the given equation, $
5x^2-7=0
,$ is equivalent to
\begin{array}{l}\require{cancel}
5x^2=7
\\\\
x^2=\dfrac{7}{5}
.\end{array}
Taking the square root of both sides (the Square Root Property), the solutions to the given equation are
\begin{array}{l}\require{cancel}
x=\pm\sqrt{\dfrac{7}{5}}
\\\\
x=\pm\sqrt{\dfrac{7}{5}\cdot\dfrac{5}{5}}
\\\\
x=\pm\sqrt{\dfrac{35}{25}}
\\\\
x=\pm\dfrac{\sqrt{35}}{\sqrt{25}}
\\\\
x=\pm\dfrac{\sqrt{35}}{\sqrt{(5)^2}}
\\\\
x=\pm\dfrac{\sqrt{35}}{5}
.\end{array}