#### Answer

Points A, B, and C are collinear.

#### Work Step by Step

To calculate the slope between points $(x_1,y_1)$ and $(x_2,y_2)$, we use the formula:
$slope=m=\frac{y_2-y_1}{x_2-x_1}$
We calculate the slope between the points $A(1,-2)$ and $B(3,-1)$:
$slope=\frac{-1-(-2)}{3-1}=\frac{1}{2}$
Next, we calculate the slope between the points $B(3,-1)$ and $C(5,0)$:
$slope=\frac{0-(-1)}{5-3}=\frac{1}{2}$
Finally, we calculate the slope between the points $A(1,-2)$ and $C(5,0)$:
$slope=\frac{0-(-2)}{5-1}=\frac{2}{4}=\frac{1}{2}$
Since the three slopes are the same, the three points A, B, and C must be collinear.