$\because y=4e^x\left(e^{-5t}\right)$ (given)

$=4e^{x-5t}$

$\because$ It is a form of $y=f\left(ax\pm bt\right)$

So, it represents a progressive wave, propagating in positive $\text{x}$-axis direction because coefficients of $x$ and coefficient of $t$ have opposite sign.

$\because$ Speed of a wave, $v=\frac{\mathrm{C}\mathrm{o}\mathrm{e}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }t}{\mathrm{C}\mathrm{o}\mathrm{e}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }x}=\frac{5}{1}=5 {\text{m s}}^{-1}$