Given f(x) = x3 + ax2 + 5x + c, and that f(2)=0 and f(-1)=0, find the value of a.

Substitute $x=2$ into the function $f(x) = x^3 + ax^2 + 5x + c$:

$$f(2) = (2)^3 + a(2)^2 + 5(2) + c = 0$$ $$8 + 4a + 10 + c = 0$$ $$4a + c + 18 = 0 \quad (*)$$

Substitute $x=-1$ into the function $f(x) = x^3 + ax^2 + 5x + c$:

$$f(-1) = (-1)^3 + a(-1)^2 + 5(-1) + c = 0$$ $$-1 + a - 5 + c = 0$$ $$a + c - 6 = 0 \quad (**)$$

From equation $(*)$, we have $4a + c = -18$.
From equation $(**)$, we have $a + c = 6$.

Subtract equation $(**)$ from equation $(*)$:

$$(4a + c) - (a + c) = -18 - 6$$ $$4a - a + c - c = -24$$ $$3a = -24$$ $$a = \frac{-24}{3}$$ $$a = -8$$

The value of $a$ is $\boxed{-8}$.