Hm, I had thought that different Variants of the same product would still count as the "same" product for discounts; apparently I was mistaken in that, but I'll ask Development if there's any way they could make it work that way, as that seems sensible.
Meanwhile, you might consider making an automatic (no-code) discount for All Cart Items with Min. Item Quantity=5, so any 5 or more items added to the cart would take a percentage off the whole-order Item Total.
If that won't work (say, if you also sell small-dollar accessories that you don't want triggering the discount), you could keep the product-specific discount requiring a code, but remove the Min. Item Quantity; then you'd just have to catch orders where the code was redeemed without actually having 5 or more qualifying items in the order.