Understanding battery capacity with solenoid application
You're some of the way there in your thinking. To operate, each solenoid needs to be connected to a 5 V power supply. You say its a 0.93 W solenoid so it will draw around 0.186 A from that supply (P = V x A).

So to operate 15 at once, you need a power supply capable of providing 5 V at 2.79 A. That's a steady-state current, a sort of 'up and running' value.

Your 1.5 V 'D' cell supplies about 1.5 V nominal, which will drop under heavy load to a lower voltage. Therefore you could connect 4 in series to get 6 V, giving you some margin if the battery voltage drops.

The problem is that a typical alkaline cell won't give you 2.8 A peak. Revise your question to detail the battery you have and I can expand on this further.