The minimum value of $2\cos x-3{\cos }^{2}x+5$  is

Minimum of value ${\cos }^{2}x=0$  but minimum of ${\cos }^{2}x=1$  when $\cos x=-1$

$\therefore$  Minimum of $2\cos x-3{\cos }^{2}x+5=2\left(-1\right)-3\left(1\right)+5=0$