${\left(-\sqrt{5}\right)}^2=5$  

 

$\sqrt[3]{5^3}=5$  

 

$\sqrt{\sqrt{{\left(-5\right)}^4}}=\sqrt{\sqrt{625}}=\sqrt{25}=5$  

 

$5\sqrt{{\left(-5\right)}^2}=5\cdot \sqrt{25}=5\cdot 5=25$  

 

$\sqrt{5\sqrt{5^2}}==\sqrt{5\sqrt{25}}=\sqrt{5\cdot 5}=\sqrt{25}=5$