I'm pretty sure they are both FS1r2 sockets. Really want to verify with anyone out there that has done it.
HP Probook 645 G1
even if the CPU may physically fit and the tdp matches, the a4-4300m and a10-5750m are different generations of CPUs. It's not certain, that HP provided a compatible BIOS for your Probook. You could still try, I would at least install the latest BIOS in advance.
There are so many things to consider. One big one is that if that bios does not support that cpu or even if the cpu can even be removed and is not soldered to the board for instance.
The cooling solution is likely not up to the task of a faster processor. So very likely it could throttle leaving you potentially worse performance.
Or the PSU can't supply proper power over heating your brick and causing failure or at best just creating system instability.
Laptops just are typically designed only for the configuration they are supplied as.
With laptops if you need performance getting another model is best.
However if you just like to tinker by all mean go for it.
I googled the laptop. Its socketed (FS1r2). The default CPU and the desired upgrade have a 35w TDP.
The question remains, whether the BIOS can handle the newer CPU (with more cores).
This CPU Upgrade website has your HP Laptop model showing all the CPUs that are compatible: https://www.cpu-upgrade.com/mb-HP/ProBook_645_G1.html
But I would highly suggest that you still double check with HP Support .
NOTE: The A10-5750M seems to be supported for an upgrade for your laptop.
Definitely ask. Showing what they supported DOES NOT MEAN THEY ARE UPGRADEABLE. It means they sold them with those options. It also may be in addition to that better cpu they also used better cpu cooling option as well that you won't have on your old model and likely at this point may not be able to buy either.
Wattage being the same does not mean not hotter. My ryzen 3600 is 65 watt and my 3700x is too. Yet one has 4 threads more and is higher clocked thus needing a better cooler. So yes it is possible you can drop in the processor it is also possible the bios may not support it ever and it possible the cooling won't either.
Again if you want to tinker go for it. Just don't be disappointed if it doesn't work out. Unless HP sells you what is needed and says yes it will work.
I have successfully upgraded this notebook with the A10-5750M. Make sure you have updated the BIOS from HP, and it will work.
Thanks for verifying to the OP that you can upgrade that HP laptop with the A10-5750M CPU.
NOTE: After upgrading to the new more powerful CPU did your laptop overheat more often or it was the same?
Well I upgraded almost as soon as I got it, so not too sure. When it's at high CPU and GPU usage, it will get up to about 95C according to CoreTemp. Of course, YMMV depending on your particular A10-5750M - silicon lottery - etc. - so make sure the thermal compound is good.