How to calculate the steady state response $y_{ss}(t)$ of a LTI system given the Laplace transform $Y(s)$?
For these calculations, it is better to give the Wolfram Alpha answers:

inverse Laplace transform 1/(s*(s^2 + 4*s + 5)) 

Which gives the correct expression, consistent with the Final Value expression of 1/5:

$$\frac{1}{5} - \frac{1}{5} e^{-2 t} (2 sin(t) + cos(t))$$

This is very different from the complex (phasor) expression, which could inexplicably have a 1/10, but when evaluated it is still 1/5:

$$\frac{1}{10} i (e^{(-2 - i) t} ((2 + i) e^{2 i t} + (-2 + i)) - 2 i)$$