To multiply \( \frac{7}{10} \) by \( 5 \), we can express \( 5 \) as a fraction:
\[ 5 = \frac{5}{1} \]
Now, we multiply the two fractions:
\[ \frac{7}{10} \times \frac{5}{1} = \frac{7 \times 5}{10 \times 1} = \frac{35}{10} \]
Next, we simplify \( \frac{35}{10} \):
\[ \frac{35 \div 5}{10 \div 5} = \frac{7}{2} \]
Now, to convert \( \frac{7}{2} \) to a mixed number, we divide \( 7 \) by \( 2 \):
\[ 7 \div 2 = 3 \quad \text{(whole number part)} \] \[ 7 - (2 \times 3) = 1 \quad \text{(remainder)} \]
Thus, \( \frac{7}{2} \) can be written as:
\[ 3 \frac{1}{2} \]
Therefore, the final answer is:
\[ \boxed{3 \frac{1}{2}} \]