Thanks for giving me the real hint I needed:

Also, make sure you take all the binary in one long sequence, and not 8 sequences of 5 bits otherwise the conversion won't work (since it should give 5 characters at the end and not 8).

Well that settles my problem...I understood this:

Once all the pieces will be in the proper order, I need you to input in the system the whole coaster, piece by piece. There are 5 pieces per section, each one measuring 6 feet of ground space.

to mean that all 5 pieces of a section were 1/8 of it's solution. So I'd have to convert the solution another time like this:
01010
11001
10110
10100
00010
11010
11010
11001

01110111
11000111
00110000
10101110
01000001

to get the 5 seperate characters, but would only get "wÇ0®A".

It never crossed my mind, that it's easier and I already had the solution with those 40 zeros and ones....🙄