Answer
Possible zeros: $1, -1, 5, -5$
Work Step by Step
The Rational Zero Theorem states that the possible zeros for a polynomial function with integer coefficients can be given by the ratio between the factors of the constant term and the factors of the leading coefficient which is to say, in this exercise, $5$ and $1$ respectively. Therefore, we list the possible factors of each one:
$$5: \frac{+}{}1, \frac{+}{}5$$
$$1: \frac{+}{}1$$
and determine all possible combinations for the ratio:
$$\frac{5_{factors}}{1_{factors}} : \frac{\frac{+}{}1}{\frac{+}{}1}, \frac{\frac{+}{}5}{\frac{+}{}1}$$
Therefore, the possible zeros are: $1, -1, 5, -5$
