Докажите неравенство: с+5/с + с+5/5 < 4, при с < 0

Решите задачу:

$\frac{c+5}{c} + \frac{c+5}{5} \ \textless \ 4 \\ \frac{c+5}{c} + \frac{c+5}{5} - 4 \ \textless \ 0 \\ \frac{5(c+5)+c(c+5)-20c}{5c} \ \textless \ 0 \\ \frac{5c+25+c^2+5c-20c}{5c} \ \textless \ 0 \\ \frac{(5-c)^2}{5c} \ \textless \ 0 \\ \left \{ {{(5-c)^2 \ \textless \ 0} \atop {5c\ \textgreater \ 0}} \right. \to \left \{ {{(5-c)^2 \ \textgreater \ 0} \atop {5c\ \textless \ 0}} \right. \\ x \to (-\infty, 0)$