If $\log _{b} 5=0.7, \log _{b} 3=0.5$, evaluate the following. \[ \log _{b} \frac{5}{3} \] \[ \log _{b} \frac{5}{3}= \] (Simplify your answer.)

Step 1 ：Given that \(\log _{b} 5=0.7\) and \(\log _{b} 3=0.5\), we are asked to evaluate \(\log _{b} \frac{5}{3}\).

Step 2 ：Using the properties of logarithms, we know that \(\log_b \frac{a}{c} = \log_b a - \log_b c\).

Step 3 ：Substituting the given values, we get \(\log_b \frac{5}{3} = \log_b 5 - \log_b 3 = 0.7 - 0.5\).

Step 4 ：Solving the above expression, we get \(\log_b \frac{5}{3} = 0.2\).

Step 5 ：Thus, the value of \(\log _{b} \frac{5}{3}\) is approximately \(\boxed{0.2}\).