Why is the current for \$i(t)\$ \$5mA\$, not \$5e^{-\frac{t}{0.8m}}\$ mA?
I think you're stating a paradox.

\$ 5e^{-\frac{t}{0.8}} \text{ mA} \$does hold, but the question asks you to evaluate it for \$t=0\$.

So, the answer is 
$$ 5e^{-\frac{t}{0.8}}|_{t=0} \text{ mA} = 5e^{-\frac{0}{0.8}} \text{ mA} = 5 \text{ mA}$$