Find the coefficient of x⁵ in the expansion of ((1)/(p) + px)⁷.

Step 1: Find the coefficient of $x^5$ in the expansion of $\left(\frac{1}{p} + px\right)^7$.
The general term in the binomial expansion of $(a+b)^n$ is given by $T_{r+1} = \binom{n}{r} a^{n-r} b^r$.
For $\left(\frac{1}{p} + px\right)^7$, we have $n=7$, $a=\frac{1}{p}$, and $b=px$.
The general term is:

$$T_{r+1} = \binom{7}{r} \left(\frac{1}{p}\right)^{7-r} (px)^r$$ $$$$