Finding minterms of a 5-var Boolean Expression having 10 terms containing NAND

Question

I have this question for my assignment and I am not getting that how can we find the minterms of this expression. It has 10 terms, it is 5 variable expression and it contains NAND.

Expression:

$F=AB'E+(BC)'DE'+(CD)'E+A'DE'+A'CDE'+A(CD)'E+AE+A(BE)'+(AC)'+BCD'$

I tried the following approach:

My Approach:

1. Eliminating NAND from the expression using Laws and Properties
2. Modifying each term to have every input/variable
3. Removing the duplicate terms using Identity Law

But this result in giving 32 minterms from 0 - 32 that is SIGMA(m0, m2, m3, m4.....m32) and if we look the expression has 5 variables and 2^n = 2^5 = 32 shows the Karnaugh Map will have 32 Cells. Therefore, if we get 32 minterms, all of the Karnaugh Map's Cells are gonna filled up and that is totally confusing me.

Kindly tell me how should I find the minterms so that I can map them on K-Map as required in my Assignment Question. The actual Question's pic is below:

Answer 1

The resulting Karnaugh map should look similar to this one:

There is a nice application online for your own experiments.

Here is an alternative form in typewriter style (without encircled blocks):

            de                     de
      00  01  11  10         00  01  11  10
 abc +---+---+---+---+  abc +---+---+---+---+
 000 | 1 | 1 | 1 | 1 |  001 | 1 | 1 | 1 | 1 |
     +---+---+---+---+      +---+---+---+---+
 010 | 0 | 0 | 0 | 1 |  011 | 1 | 1 | 1 | 1 |
     +---+---+---+---+      +---+---+---+---+
 110 | 1 | 1 | 0 | 1 |  111 | 1 | 1 | 1 | 0 |
     +---+---+---+---+      +---+---+---+---+
 100 | 1 | 1 | 1 | 1 |  101 | 0 | 1 | 1 | 0 |
     +---+---+---+---+      +---+---+---+---+

The simplified expression:

ae + a!b + !a!c + bc!d + !ad!e