I suspect that the problem is with the switching diode D2. Either this diode is defective, the wrong part, or perhaps it is interchanged with D1. D1 is a garden variety rectifier. D2 needs to be a schottky fast recovery diode. A regular diode at location D2 will not clamp the inductive kick of L1 fast enough and allow a negative voltage to be applied to both IC1 and C2. This would explain while those two parts are failing.
My suggestion is to replace IC1, D2 and C2 with known good parts. Verify the markings on D2 versus the datasheet and make sure it is oriented in the circuit correctly. From the picture, I think I see an “R” on that component. Since “R” is not part of the IN5819 part number, this must be part of some manufacturer’s number. Once these three components are populated with known good parts, then I would have all other IC removed and attempt to power the board from a 9V battery. I think one nine volt battery should be enough to run IC1 with no load. See if you get something close to a five volt output and that IC1 runs cool. If IC1 is hot and the input rail is dragging down the nine volt battery, then something else is loading the circuit.