Answer
$5.8$
Work Step by Step
In the largest triangle, where 5 is the height of the triangle, not a side,
the third angle (to the right of x)
is $60^{o}$ (sum of angles $=180^{o}).$
In the smallest right triangle (bottom),
x is opposite the right angle, so x is the hypotenuse,
5 is the leg opposite to the angle of $60^{o},$
so
$\displaystyle \sin 60^{o}=\frac{5}{x}\ \Rightarrow\ x=\frac{5}{\sin 60^{o}}$
$ x\approx$5.7735026919$\approx 5.8$
