Answer
The limit as x approaches negative infinity is positive infinity.
The limit as x approaches positive infinity is negative infinity.
Work Step by Step
The leading term is $-2x^{5}$. The multiplicity is 5, so it's odd. This means that the limits, or end behaviors, will be opposite of each other. The leading term is also negative, meaning that the graph, and subsequently the limits/end behaviors, is flipped. A regular $x^{5}$ would have end behavior of:
x -> -infinity, f(x) -> -infinity
x -> infinity, f(x) -> infinity
Since the leading term of our polynomial is negative, it flips this.
