Non-occupation probability 5kT above Fermi level

The probability that a state of energy $E$ is occupied is given by the Fermi–Dirac function

$$f(E) = \frac{1}{1 + \exp\left(\dfrac{E - E_F}{kT}\right)}$$

The probability that it is not occupied (empty) is $1 - f(E)$.

Given: $E - E_F = 5kT$.

$$\begin{aligned} f(E) &= \frac{1}{1 + e^{5}} = \frac{1}{1 + 148.41} = \frac{1}{149.41} = 0.00669 \\ 1 - f(E) &= 1 - 0.00669 = 0.99331 \end{aligned}$$

Equivalently, $1 - f(E) = \dfrac{e^5}{1 + e^5} = \dfrac{148.41}{149.41} = 0.9933$.

Answer: the probability that the state is not occupied is 0.9933 (99.33 %).

A state $5kT$ above $E_F$ (about 0.13 eV at 300 K) is almost always empty; only 0.67 % of such states hold an electron. The answer is the same at every temperature because the energy is expressed in units of $kT$.