Introduction:
A palindrome is a word or a sequence of characters which reads the same way forward and backward. In this question, we need to find the number of 5-lettered palindromes that can be formed using the letters from the English alphabet.

Solution:
To solve this problem, we need to consider the following cases:

Case 1: The middle letter is fixed
If we fix the middle letter of the palindrome, then there are 26 choices for that letter. The first and last letters of the palindrome must be the same, so there are 26 choices for each of those letters. For the second and fourth letters, we can choose from the remaining 25 letters. Therefore, the total number of palindromes in this case is:

26 x 26 x 25 x 26 x 26 = 44,220,800

Case 2: The middle letter is not fixed
If the middle letter is not fixed, then we have 26 choices for the first letter, 26 choices for the last letter, and 25 choices for the second and fourth letters. The third letter must be the same as the first letter, so there is only one choice for that letter. Therefore, the total number of palindromes in this case is:

26 x 25 x 1 x 25 x 26 = 16,2500

Total number of palindromes:
The total number of palindromes is the sum of the palindromes in case 1 and case 2:

44,220,800 + 16,2500 = 44,446,300

However, we need to divide this number by 2, because we have counted each palindrome twice (once for the first and last letters being the same, and once for the last and first letters being the same). Therefore, the final answer is:

44,446,300 / 2 = 22,223,150

Rounding to the nearest whole number, we get the answer:

Answer: 263.