A 5:3 codes is a systemboard problem.
This is what HP says:
The red light blinks five times, and then three, short white light blinks
This condition indicates the embedded controller cannot reach the BIOS within the established time limit.
Remove all accessory devices from the notebook and try to start it.
Contact HP service.
Try a power refresh to hopefully get it working again.
i). Switch off the laptop and disconnect the charger from the laptop if connected.
ii). Disassemble the laptop and disconnect the battery from the systemboard. You don’t have to remove the battery, simply disconnect it.
iii) Remove the RTC coin cell battery from the systemboard. Remember its orientation for when you reinsert it later. Usually it is +ve on top as marked on the battery
Here’s the maintenance and service guide for the laptop, taken from this webpage. This details the necessary pre-requisite steps to access and remove the components. The RTC battery is not mentioned but when you have the laptop open and can access the systemboard, you will see it.
iv). Press and hold the laptop’s Power on button for a full 30 seconds and then release it. This will restore the BIOS to its default settings, in case a corrupted BIOS was the cause of the problem.
v). Reinsert the RTC coin cell battery, (remember orientation), reconnect the main battery, re-assemble the laptop, connect the charger and turn on the laptop and check.
If it starts OK there may be a message about the date and time being incorrect. This is normal as the BIOS has been reset. Once the D&T have been adjusted, the message won’t appear the next time the laptop is started.
If the error code is still there, then commiserations, as there is a problem on the systemboard. You may either have to find the schematics for the systemboard and try to work out what’s wrong or contact a reputable, professional laptop repair service.