Why does the Acer Travelmate Gen5 Core i5 P645-S laptop screen takes 15 seconds to light up?

This could be a software or a hardware problem that needs analyzing, make sure that you have the latest Win-10 updates and the latest 22H2 version and OS build 19045.5371 installed to make sure that the graphics are up to date, but remember that this is a 7 years old laptop and it could be that its battery, which should have been replace and done a long time ago, or its eDP cable that connects the mainboard to the screen, and that the lid is open and closed so many times, and is under constant bending, might have been damaged and its data strands could contribute to a delayed graphics and might need to be replaced or its plugs data pins could be shorted or the last thing that could be faulty is the actual screen. So you need to check all that out, as we can't give you an exact diagnosis without actually and physically inspecting your laptop. Good luck.

eDP oem cable fitted to this laptop that might need to be replaced.

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