Is $(-3)^n + 5^n$ monotone? How can I establish if this sequence is monotone?

If it isn't, is it permanently monotone from a certain n* to infinite?
Suppose
$$(-3)^{n+1} + 5^{n+1} &lt; (-3)^n + 5^n.$$
Then $4\cdot 5^n&lt;4\cdot (-3)^n$. Hence $5^n&lt;(-3)^n$, a contradiction.
Hint:

$$\frac{(-3)^{n+1}+5^{n+1}}{(-3)^n+5^n}=\frac{5^{n+1}\left(\left(-\frac35\right)^{n+1}+1\right)}{5^n\left(\left(-\frac35\right)^n+1\right)}\xrightarrow[n\to\infty]{}5&gt;1$$