Screw Terminal Block Amperage Ratings
The 15 A rating is the current capability across each bus connection and on each terminal. So you can't use two terminals to take 30 A in and ferry it to two further-down terminals to take that 30 A out.

Your description sounds like you want to take a single supply in and route out several 5 A supplies out. You can bring in several 15 A supplies, each on its own wire and near three terminals loading with 5 A. Even though these will all be connected to the same common bus-bar, distributing the supplies and loads that way will be fine. (I designed a similar arrangement recently, routing out 40 A to a variety of loads.)