Problem- Find the terms through x^5 in the Maclaurin series for f(x)=e^(-x) * cos(x)

After trying to find f'(x), f''(x), f'''(x), and so on, the derivatives seemed overly complex. I heard that it is possible to use known Maclaurin series (e.g. e^(-x) and cos(x) separately) and then perform multiplications, divisions, etc. How would I combine them?

Thanks!