V000238010 is the part number of the system board for the laptop and it does have a removable cpu.
your best bet is to email toshibia ask them what is the max speed and or voltage that the cpu can be used on this system board and laptop. if not see if you can find a local toshiba repair place see if they have the cd repair book for your laptop., in it is a listing of all spare parts. one of them may be a faster cpu.
myself i would add more ram and max your ram out if you can first.then i would back your data up and put a clean image if you havent done it yet in a while also use hdtune check that your hard drive still good in the laptop. i would then if it still slow wait for the newer skylake laptops and see if you can donate the old...