To find the product of \(\sqrt{36}\) and \(\frac{5}{3}\), we first calculate \(\sqrt{36}\):
\[ \sqrt{36} = 6 \]
Now, we multiply this result by \(\frac{5}{3}\):
\[ 6 \times \frac{5}{3} = \frac{6 \times 5}{3} = \frac{30}{3} = 10 \]
Thus, the product of \(\sqrt{36}\) and \(\frac{5}{3}\) is \(\boxed{10}\).