jmc

The slope of the line through $(0,3)$ and $(-8,0)$ is $(0-3)/(-8-0)=3/8$. If $(t,5)$ is also on this line, then the slope of the line through $(t,5)$ and $(0,3)$ must also be $3/8$. Therefore, we must have $$\frac{3-5}{0-t}=\frac{3}{8}⟹\frac{2}{t}=\frac{3}{8}⟹(2)(8)=3(t)⟹t=\boxed{\frac{16}{3}}.$$