If $\left|\overline{a}\right|=2,\left|\overline{b}\right|=3$  and $|2\overline{a}-\overline{b}|=5$  then $|2\overline{a}+\overline{b}|$  equals to

$|2\overline{a}-\overline{b}|=5$    

SOBS

$4{\left|\overline{a}\right|}^2+{\left|\overline{b}\right|}^2-4(\overline{a}.\overline{b})=5^2$

$4{\left(2\right)}^2+{\left(3\right)}^2-4(\overline{a}.\overline{b})=25$

$25-4(\overline{a}.\overline{b})=25$  $\Rightarrow -4(\overline{a}.\overline{b})=0$   

$\overline{a}.\overline{b}=0\Rightarrow \overline{a}\perp \overline{b}$

$|2\overline{a}+\overline{b}|=\sqrt{4{\left|\overline{a}\right|}^2+{\left|\overline{b}\right|}^2+4(\overline{a}.\overline{b})}=\sqrt{4{\left(2\right)}^2+3^2+0}=\sqrt{25}=5$