1. Interpret the condition

Five distinct letters are chosen from the 26 English alphabets and then arranged in alphabetical order.

This means that once the 5 letters are chosen, their arrangement is fixed. So we only need to count the number of 5-letter subsets whose 3rd (middle) letter is $M$.

2. Position of $M$ in alphabetical order

If $M$ is the middle letter, then:

• exactly 2 chosen letters must be before $M$, and
• exactly 2 chosen letters must be after $M$.

3. Count letters before and after $M$

Letters before $M$: $A, B, C, D, E, F, G, H, I, J, K, L$ There are $12$ such letters.

Letters after $M$: $N, O, P, Q, R, S, T, U, V, W, X, Y, Z$ There are $13$ such letters.

4. Choose the required letters

We must choose:

• 2 letters from the 12 before $M$,
• 2 letters from the 13 after $M$.

Hence total ways: $\binom{12}{2}\binom{13}{2}$

Now compute: $\binom{12}{2} = \frac{12\cdot 11}{2} = 66$ $\binom{13}{2} = \frac{13\cdot 12}{2} = 78$

Therefore, $66 \times 78 = 5148$

5. Match with options

Thus the required number of ways is: $\boxed{5148}$

So the correct option is B.