Example 7 The equation $\frac{1}{5} \log _{2} x=\sin (5 \pi x)$ has how many real roots?
Dividing  Just to determine the number of roots, the basic method is to use the graph of the function to solve by combining numerical and graphical analysis.
Solution The number of real roots of the original equation is the number of intersection points of the graphs of the two functions $y=\frac{1}{5} \log _{2} x$ and $y=\sin (5 \pi x)$. Since $|\sin x| \leqslant 1$, we only need to consider $\frac{1}{32} \leqslant x \leqslant 32$.
(1) When $\frac{1}{32} \leqslant x<1$, since the smallest positive period of the function $y=\sin (5 \pi x)$ is $\frac{2}{5}$, the graph of the function $y=\sin (5 \pi x)$ appears twice within its range, with four intersection points below the x-axis;
(2) When $1<x \leqslant 32$, the length of the range is $\frac{155}{2}$ times the period. Since $\sin 5 \pi x=0$ when $x=1$, there are $77 \times 2=154$ intersection points;
(3) When $x=1$, the two functions also have one intersection point.
In summary, the original equation has a total of $4+154+1=159$ real roots.