form a polynomial f(x) with real coefficients having the given degree and zeros?

If the coefficients are to be real, and if -i is a zero, then i is also a zero. Likewise, if -4+i is a zero then -4-i is also a zero.

Use the factor theorem to convert the five zeros into factors:

(x + 1) (x + i) (x - i) (x + 4 - i) (x + 4 + i)

Multiply these five factors together. (It's easier to multiply the pairs of complex conjugates first.):

x^5 + 9x^4 + 26x^3 + 26x^2 + 25x + 17