"He who marches out of step hears another drum." ~ Ken Kesey
Wait, why couldn't you do it as halftones?
Give him a handfull of Gray ink (-or- grey) and ask him to divide it up into the 5 shades he wants.
Had an arugment today with a customer that has a design with 5 shades of the same color grey, priced it as a 5 but the customer (who knows more about my job than I do...) proceeded to tell me Im ripping them off it's 1 color just different shades. No matter how I explained it, it wasnt doing any good. I think from here on out I'm going to ditch "colors" and go with "screens" but that might be even more confusing for the stupid. 1/2 tones wasn't an option. The kicker is when I get asked if white and black are considered "colors"
Maybe give them a tour of your shop. Show them how the process works...
This really does sound like the customer had a lack of understanding of the process but why did it matter how many screens colors etc. after the fact. Did your client agree to the charges up front and sign off on everything befor you ordered shirts and printed?
but black and white aren't colors, so don't bill him for those