To simplify the given Boolean expression, we will follow these steps:

Expression:

$X = A'B'C'D'E' + A'B'CD'E' + A'BCD'E' + A'BC'D'E' + A'B'C'D'E + A'BCD'E + A'BCDE + AB'C'D'E + AB'C'D'E + ABCD'E + ABCDE + AB'CDE$

Step 1: Group terms for simplification

Group terms based on their common literals. Let’s rewrite:

1. $A'B'C'D'E'$ and $A'B'C'D'E$
2. $A'B'CD'E'$
3. $A'BCD'E'$ and $A'BCD'E$
4. $A'BC'D'E'$
5. $A'BCDE$
6. $AB'C'D'E$
7. $ABCD'E$
8. $ABCDE$
9. $AB'CDE$

Step 2: Apply simplification rules

1. $A'B'C'D'E' + A'B'C'D'E$: $A'B'C'D'(E' + E) = A'B'C'D'$

2. $A'B'CD'E'$ remains as is.

3. $A'BCD'E' + A'BCD'E$: $A'BCD'(E' + E) = A'BCD'$

4. $A'BC'D'E'$ remains as is.

5. $A'BCDE$ remains as is.

6. $AB'C'D'E$ remains as is.

7. $ABCD'E$ remains as is.

8. $ABCDE$ remains as is.

9. $AB'CDE$ remains as is.

Step 3: Combine simplified terms

The simplified Boolean expression is:

$X = A'B'C'D' + A'B'CD'E' + A'BCD' + A'BC'D'E' + A'BCDE + AB'C'D'E + ABCD'E + ABCDE + AB'CDE$

Step 4: Combine further if possible

Inspect for more common terms:

• The terms $A'B'C'D'$, $A'B'CD'E'$, $A'BCD'$, $A'BC'D'E'$, and $A'BCDE$ cannot combine further as they differ in too many variables.
• Similarly, $AB'C'D'E$, $ABCD'E$, $ABCDE$, and $AB'CDE$ remain distinct.

Final Simplified Expression:

$X = A'B'C'D' + A'B'CD'E' + A'BCD' + A'BC'D'E' + A'BCDE + AB'C'D'E + ABCD'E + ABCDE + AB'CDE$

This is the most simplified version of the given Boolean expression.

Would you like me to explain any part of the process or check for further optimization?