Michael: you're correct. There is a sign error in one place, but I corrected it when I actually computed the coefficients. So the final answers are correct. Thanks for finding this. I've added annotations between 8 and 12 minutes to indicate the sign error.
Why are we evaluating b at s=-5-3j and c at s=-5+3j? Shouldn't it be the other way around since when we set the denominators of those fractions to zero, we get those values for s?