Answer
a. $n\geq50$
b. $n\geq17$
c. $n\geq10$
d. $n\geq25$
e. $n\geq50$
Work Step by Step
a. let $np\geq5\cap nq\geq5$, we have $0.1n\geq5\cap 0.9n\geq5$, so $n\geq50$
b. $0.3n\geq5\cap 0.7n\geq5$, so $n\geq16.7\approx17$
c. $0.5n\geq5\cap 0.5n\geq5$, so $n\geq10$
d. $0.8n\geq5\cap 0.2n\geq5$, so $n\geq25$
e. $0.9n\geq5\cap 0.1n\geq5$, so $n\geq50$