Simplify. Then classify by all sets to which it belongs: real, pure imaginary, complex.

$8i\left(2i–i^2\right)+\sqrt{–25}$

$$\begin{gathered} 16i^2–8i^3+5i \\ 16\left(–1\right)–8\left(–i\right)+5i \\ –16+8i+5i \\ –16+13i, \mathrm{complex} \end{gathered}$$