If this is the motherboard you mean, I would bet against it for a couple of reasons:http://www.tradetang.com/for-sale/HP-OEM-MSI-MS-7525-Boston-Motherboard-464517-001-G31-PC/129593-1922574.html
First, there are two kinds of 775 processors -- the ones built on 65nm technology and the newer kind built on 45nm technology. Some of the older 775 motherboards were made when 45nm wasn't around yet ... some of them can handle 45nm with a BIOS update and some will never be able to handle 45nm ever. Your board looks old enough that it could be one of the very early 65nm-only kind.
Second, even if it COULD handle the newer CPUs with a BIOS update, it looks like you have an HP system, and manufacturers like HP don't like to issue BIOS updates that let you support new processors. They don't make any money off of you dropping in a new CPU that you bought somewhere else; they want you to buy a whole new system from them. There have been other instances of assembly companies doing this with different components, like Dell making a motherboard that took a specially made plug so it wouldn't work with other people's power supplies, and other things of that nature.
So in a nutshell, I'm pretty pessimistic about your chances. I definitely would NOT go out and buy a q9550 or something and just drop it in.