A company claims that no more than 5% of a particular product has a defect. In a shipment of 15 units, what is the probability of receiving 3 or 4 defective units?

This cannot be answered the way the question is worded. What you need to know is the probability that a given unit is defective. All you have is a manufacturer's claim of "no more than 5%", with no statistical significance. That could imply a wide range of probailities

If the question were worded that the company claims that 5% of a particuar product has a defect, could this be worked?