My input to my TI nSpire CX CAS was:
$solve(\frac{r\cdot (p+q)}{p\cdot q}<5$ and $p>0$ and $r>0$ and $q>0,p)$
The first answer it gave was
$0<p<\frac{-q\cdot r}{r-5\cdot q}$ and $r-5\cdot q>0$ and $r>0$ and $q>0$
which is impossible.
If $r$,$q$, and $r-5\cdot q$ are all non-zero and positive then $\frac{-q\cdot r}{r-5\cdot q}$ is negative and p cannot be non-zero and both negative and positive at the same time.
The second answer after the 'or' it gave was also impossible. It gave
$0<p<min(0,\frac{-q\cdot r}{r-5\cdot q})$ and $0<r<5\cdot q$ and $q>0$
Why does it give this result? Is there a bug in the calculator?