Welcome to the forum, @ladra!
You're right - this isn't something Magento's product types are going to do out of the box. However, I'm thinking you might be able to achieve it with creative use of Magento's shopping cart price rules. Basically, you could setup a rule that if, say, 6 products matching a given criteria are found, the user gets a discount that is sufficient to make the price $5. That would allow people to buy a single shirt at full price, and then get the discount when they buy 6.
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