How to get these logic equations? (5 variable Karnaugh maps)

Forget the tools. Tools are good for doing th eroutine work once you have grabbed an understanding of the process. Otherwise you will never be able to judge the result of a tool.

I recommend that you look up K-maps in your textbook or in the Wikipedia. It is fairly well explained there.

Minimization using K-maps is done by grouping as many cells within the map as fit into a signle rectangular area. Isually there is more than one such area and they may overlap.
For each rectangular area you the:
- identify the input variables whose value is constant within that area
- set up the equation for these variables only.
Background: If an input variable can be either low or high for the same result (same rectangular area), this input variable is irrelevant for that equation.

What about the empty cells in your maps? Are they "0" or don't care? If you have don't care cells, you can set them to either "0" or "1" to maximize the size of the rectangular areas (see above) and thus minimize the size of the boolean equations.

Start with a smaller 2-by-by or 4-by-4 K-map to exercise the procedure. Then go ahead to the 4-by-8 matrix.

Show us your results and we will check them and guide you along.

But we won't do your homework.

Harald

P.S.:

What was "bad" about the tool's solution? You could have used the tools solution as a starting point for further manual optimization.