"Suppose you are the owner of a small t-shirt printing business. While conducting a cost analysis of your business, you find that at current production levels, your average total cost (ATC) is $10. You also know that if you increase production by one more unit, the marginal cost of that unit will be $5. If you produce another t-shirt" does the avg/marginal cost decrease or increase?

The answer is The average total cost of production will decrease.

Explanation:

It cannot be known to be true if the marginal cost will decrease/increase for the very next unit of production. this will depends on what point of curve of  marginal cost and the level of the current production..

However, it is certain that, is the average total cost for the next unit produced will decrease, because the ATC is defined as total cost/output.

The next unit produced would definitely reduce the ATC, Since  the total output  is in the denominator,  this cost would move over an output larger.