Seems like the AC adapter is not recognized.When the AC adapter is plugged into the laptop, the charging light will not turn on
It could be the adapter or it could be the charging socket on the motherboard.
ASUS X555L came out in May 2015
Do you ordinarily unplug the adapter every night?When I unplugged the AC adapter for the night
If it were the battery, you'll still see some sort of charging light. That's not to say that the battery is still good. Since it might be close to 5 years old, the battery might need replacing too but I don't think that is the main issue.
Remove the battery. Plug in the AC adapter and plug it into the wall. Does the computer power up?