Answer :

To determine whether the difference in heights between Kangchenjunga and Naltar Peak is less than 500 feet, we need to perform the following steps:

1. Identify the Heights:
- The height of Kangchenjunga is 28,169 feet.
- The height of Naltar Peak is 15,385 feet.

2. Calculate the Difference in Heights:
- Subtract the height of Naltar Peak from the height of Kangchenjunga.
- [tex]\[ \text{Height difference} = 28,169 \, \text{feet} - 15,385 \, \text{feet} \][/tex]

3. Perform the Subtraction:
- The difference comes out to be:
- [tex]\[ 28,169 - 15,385 = 12,784 \, \text{feet} \][/tex]

4. Compare the Difference to 500 Feet:
- We need to check if 12,784 feet is less than 500 feet.

From the steps above, the difference in height between Kangchenjunga and Naltar Peak is 12,784 feet, which is much greater than 500 feet. Therefore, the height difference is not less than 500 feet.

Conclusion:
The difference in heights between Kangchenjunga and Naltar Peak is 12,784 feet, and thus, it is not less than 500 feet.