\[\boxed{\text{216.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[Пусть\ x - первое\ число,\ y -\]
\[второе\ число.\]
\[Составим\ систему\ уравнений:\]
\[\left\{ \begin{matrix} x = y + 5\ \ \ \ \ \ \ \ \ \ \ \\ x^{3} = y^{3} + 3185 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow (y + 5)^{3} = y^{3} + 3185\]
\[y^{2} + 5y - 204 = 0\]
\[D = 25 + 4 \cdot 204 = 841\]
\[y_{1,2} = \frac{- 5 \pm 29}{2},\ \ \]
\[y_{1} = 12;\ \ \ \ \ \ \ \ y_{2} = - 17;\]
\[y_{1} = 12 \Longrightarrow x_{1} = 12 + 5 = 17;\]
\[y_{2} = - 17 \Longrightarrow x_{2} = - 17 + 5 =\]
\[= - 12.\]
\[Ответ:12\ и\ 17\ или\ \ \ \]
\[( - 12)\ и\ ( - 17).\]