Here are the roots here......http://www.wolframalpha.com/input/?i=solve+x^5++-160x+-128+%3D+0
Just assign each "real" root to a different variable, take the 5th power of each, and sum your answers.
P.S. (The sum of the non-real roots raised to the 5th power is about 160 .....it actually may be 160 exactly....I used Wolfram Alpha to find the roots....and they may have been "rounded")