Do you know Mr. gamma

$\begin{aligned} 2.5! + 3.5! & = \Gamma\left(\frac{7}{2}\right) + \Gamma\left(\frac{9}{2}\right) \quad \quad \small \color{#3D99F6}{\text{Gamma function }\Gamma(x+1) = x!} \\ & = \frac{5}{2}\Gamma\left(\frac{5}{2}\right) + \frac{7}{2}\Gamma\left(\frac{7}{2}\right) \quad \quad \small \color{#3D99F6}{\Gamma(1+x) = x\Gamma(x)} \\ & = \frac{1}{2} \times \frac{3}{2} \times \frac{5}{2} \times \color{#3D99F6}{\Gamma\left(\frac{1}{2}\right)} + \frac{1}{2} \times \frac{3}{2} \times \frac{5}{2} \times \frac{7}{2} \times \color{#3D99F6}{\Gamma\left(\frac{1}{2}\right)} \quad \quad \small \color{#3D99F6}{\Gamma\left(\frac{1}{2}\right) = \sqrt{\pi}} \\ & = \frac{135}{16}\color{#3D99F6}{\sqrt{\pi}} \\ & \approx \boxed{14.955} \end{aligned}$

use the gamma function and the fact that $\Gamma(x+1)=x\Gamma(x)$ until you reach $\Gamma(.5)$ which is known,through basic integration ,to be equal to $\sqrt{\pi}$