Yao Ming is $7\text{ ft and }5\text{ in}$ tall. His basketball hoop is $10$ feet from the ground. Given that there are
$12$ inches in a foot, how many inches must Yao jump to touch the hoop with his head?
1. Convert Yao Ming's height from feet and inches to inches:
   \[
   7 \text{ ft} + 5 \text{ in} = 7 \times 12 \text{ in/ft} + 5 \text{ in} = 84 \text{ in} + 5 \text{ in} = 89 \text{ in}
   \]

2. Convert the height of the basketball hoop from feet to inches:
   \[
   10 \text{ ft} = 10 \times 12 \text{ in/ft} = 120 \text{ in}
   \]

3. Calculate the difference in height between the basketball hoop and Yao Ming's height to determine how many inches he must jump to touch the hoop with his head:
   \[
   120 \text{ in} - 89 \text{ in} = 31 \text{ in}
   \]

The final answer is \(\boxed{31}\) inches.