$h(x) = (x - r_1)(x - r_2)(x - r_3)$

Given the zeros are $-5, 6,$ and $7$: $h(x) = (x - (-5))(x - 6)(x - 7) = (x + 5)(x - 6)(x - 7)$

Finding the Constant Term $c$

The standard form of the polynomial is: $h(x) = x^3 + ax^2 + bx + c$

Notice that evaluating $h(0)$ leaves only the constant term $c$: $h(0) = 0^3 + a(0)^2 + b(0) + c = c$

Now evaluate $h(0)$ using the factored form: $c = h(0) = (0 + 5)(0 - 6)(0 - 7)$ $c = (5)(-6)(-7) = (5)(42) = 210$

Thus, the value of $c$ is 210.