\[n(12 - n) - 5 =\]
\[= 4n - n(10 + (n - 3))\]
\[12n - n^{2} - 5 =\]
\[= 4n - 10n - n(n - 3)\]
\[12n + 6n - n^{2} - 5 = - n^{2} + 3n\]
\[18n - n^{2} + n^{2} - 3n = 5\]
\[15n = 5\]
\[n = \frac{5}{15}\]
\[n = \frac{1}{3}.\]