Solution:
To find the polynomial with roots at -1/2 and 5/3, we can use the fact that if a polynomial has a root at a particular value, then the polynomial can be divided by the binomial (x - root) without leaving a remainder.

(x + 1/2)(x - 5/3)
(x + 1/2)(x - 5/3) = x^2 - (5/3)x + (1/2)x - (5/6) = x^2 - (4/6)x - (5/6)
x^2 - (4/6)x - (5/6) = x^2 - (2/3)x - (5/6)

Therefore, the polynomial with roots at -1/2 and 5/3 is x^2 - (2/3)x - (5/6).