To multiply the fractions \( \frac{7}{5} \) and \( \frac{4}{3} \), you multiply the numerators together and the denominators together:
\[ \frac{7 \times 4}{5 \times 3} = \frac{28}{15} \]
Now, to convert \( \frac{28}{15} \) to a mixed number, we divide 28 by 15.
28 divided by 15 is 1 with a remainder of 13. Thus, we can express it as:
\[ 1 \frac{13}{15} \]
So, the answer is:
\[ 1 \frac{13}{15} \]