\[\boxed{\mathbf{5}.}\]
\[1)\ 5n\left( 0,2n - 2n^{2} - \frac{1}{3}p \right) = n^{2} -\]
\[- 10n^{3} - \frac{5}{3}pn = - 10n^{3} + n^{2} -\]
\[- 1\frac{2}{3}\text{pn}\]
\[2)\ \left( 4x - 1\frac{1}{3}xy - 2y \right) \cdot\]
\[\cdot \left( - 1\frac{1}{2}x^{2} \right) =\]
\[= \left( 4x - \frac{4}{3}xy - 2y \right) \cdot \left( - \frac{3}{2}x^{2} \right) =\]
\[= - 6x^{3} + 2x^{3}y + 3x^{2}y\]