Flashing P0305 Code on 2002 Cadillac DTS - Misfire After Spark Plug Repair

I own a 2002 Cadillac DTS and recently experienced a flashing P0305 OBD-II fault code. The issue started after the #5 spark plug blew out, requiring thread repair and replacement of the spark plug, boot, coil pack, and fuel injector. I drove slowly home during the incident and monitored all gauges—no oil or temperature issues were observed. After fixing the components, the check engine light remained on initially but was later cleared. However, under certain driving conditions (such as acceleration), the P0305 code begins to flash intermittently, then clears within one to two minutes. The car now exhibits a slight misfire and reduced power during operation. I’ve already checked wiring for the fuel injector using a NOID light and confirmed no visible faults. The battery drained while the vehicle was off, and I attempted to start it with a jump starter before realizing the battery had frozen—this may have contributed to electrical stress. After recharging, the battery is functional and the car starts easily. I’m now considering whether the Powertrain Control Module (PCM) could be damaged due to improper use of a jump starter or if there’s an underlying mechanical issue. I’ve performed basic diagnostics but am unsure how to confirm if the PCM is faulty or if the misfire stems from a compression problem. A compression test is next on my list, but I’d like to know whether the intermittent flashing of P0305 indicates a sensor issue, fuel delivery problem, or mechanical failure. Any advice on what diagnostic steps to take—especially live data readings via an OBD-II scanner? Also, what should the appearance of the #5 spark plug be (wet, dry, black, tan), and was an AC Delco plug used during replacement? Is there any sign of coolant loss that might point to a cylinder head or gasket issue?