Hi Al Hill! Manufacturer of motherboard is Toshiba I guess. I don't really know that much about computers. My laptop is Toshiba Satellite C855-1WX but I don't know what "system model number" is neither how to find it Could you tell me how do i make it?
You need to contact Toshiba and ask them what processors are compatible with their bios. Then you can select from those processors.
Being socket compatible is not enough. The upgrade processor must also be chipset and BIOS compatible. Only toshiba can tell you what their bios supports.