5. The popular gear-changing bicycles nowadays have several gears with different numbers of teeth installed on the drive shaft and the rear shaft. By connecting different combinations of gears with a chain, several different speeds are achieved through various gear ratios.
“Hope” brand gear-changing bicycles have three gears on the drive shaft, with the number of teeth being $48,36,24$; the rear shaft has four gears, with the number of teeth being $36,24,16,12$. Question: How many different speeds does this type of gear-changing bicycle have?
5.【Solution】Calculate all gear ratios and list them in a table:
\begin{tabular}{|c|cccc|}
\hline Main & 36 & 24 & 16 & 12 \\
\hline 48 & $\frac{4}{3}$ & 2 & 3 & 4 \\
\hline 36 & 1 & $\frac{3}{2}$ & $\frac{9}{4}$ & 3 \\
\hline 24 & $\frac{2}{3}$ & 1 & $\frac{3}{2}$ & 2 \\
\hline
\end{tabular}

There are 4 pairs of identical gear ratios: $1, \frac{3}{2}, 2, 3$. Removing the repeated gear ratios, 8 different ratios remain, so there are 8 different speeds in total.