All laptops are built with the GPU onboard.
Actually,, that's not always true,.... not all laptops, in fact the majority of laptops have an actual GPU (let's call it) Duaghterboard (that is what it is really).
They can be upgraded (rarely, but sometimes) and changed out if they go bad.
You have to have a really crappy laptop to have a GPU that is soldered to the motherboard. Or concidered Onboard.
GPU's are no longer so reliant on the CPU (even in laptops),,, they are not the Video Cards of old.
Hence the term GPU (Graphical Processing Unit) they have PU's (Processing Units) on the video card itself to take the load off the CPU (Central Processing Unit). They can however, share the RAM which can cause a problem.
With that said,,, it is a laptop,,, your bottle neck comes from the Power Supply mostly, but even this is changing.
In the OP case,, this is either a system that is just lacking the power for those games, has a problem with the GPU itself, or some other part of the system, or drivers or corrupt OS.
I will agree that lowering the settings will give better performance.
And after some thought,,, that t5800 is not all that fast a CPU, and yes, this will have an impact on the ability to play some games. The GPU is not all that great either.
Maybe this will help