Answer:
No. 5x and 5x² are not like terms.
When a variable is raised to two different powers, they can not be added together.
Another way to look at it is to note that:
5x + 5x² ≡ 5x(1 + x)
It is more obvious there that 1 and x are not like terms, thus neither are 5x and 5x², though they do have common factors.
