It looks the the original supply's power connector is unplugged and something else is powering the computer? If it was another supply, it could have contributed, possibly not to the initial tant failure as this happens frequently (assuming it was connected properly) but definitely contributed to the spectacular nature of the failure. Also now you will need to check for damaged pcb tracks & connectors.
That exploding/burning tant is one of the worst I have seen.
As mentioned on another thread, the maximum amount of power that can be transferred to a shorted tant cap (or any load) occurs when the resistance of the capacitor equals the internal resistance of the power supply itself, and at that point the power supply will be loaded down to half its unloaded value. Power supplies with sensing & protective systems though, generally shut the supply output off if it goes significantly lower than its rated voltage value or if a safe value of current & voltage are exceeded.
The original 5155 supply contains a number of protective systems (under & over voltage and current overload) and was a design masterpiece, there is an article I wrote on it in the past.
This is an area I often bring up. Vintage Computers by their nature are risky from the perspective that they contain very large numbers of increasingly difficult to replace chips. A power supply accident, over-voltage, accidental reverse polarity, poor or absent protective systems in the substitute supplies feeding them are a major risk. When people power their vintage computers from non standard psu's, there are accidents in the wings.
For example, there are many switchmode PSU's people deploy to replace vintage computer supplies they can't fix, but the protective systems are not in those supplies, but they don't think about that.
For example never underestimate the ability of a vintage analog voltage regulators, like an LM309k and its cousins to protect downstream electronics and pcb tracks. they go automatically into low current shutdown mode when shorted out, protecting not only themselves, but pcb tracks too. Shorted Tat caps present no thermal event with these.
The original 5155 is a very "safe supply" to have connected to a motherboard and cards full of precious chips, possibly better than many which followed and it also contains a unique "supply in a supply" to power the 5155's VDU. Have a read and look at its protective systems designed to, in a nutshell, "save the computer's ass" A lot of later manufacture computer PSU's and most generic types don't have nearly such an elaborate arrangement:
www.worldphaco.com/uploads/The_IBM_5155_POWER_SUPPLY.pdf
