First of all, no bumping. It's against forum rules and I'm surprised that this hasn't already been locked by a mod.
I have no idea if that particular model has a socketed CPU or not (as opposed to soldered. PGA instead of BGA), but I assume that since you took it apart you think it is. If it wasn't, you would be stuck with what you have.
Anyway, an i7-2670qm would be an option, if it'll work. i7qm's are the only ones that would make any sense to upgrade to. Not much difference in an i5m and i7m (almost none).
The i7-2670qm came in another recent DV6 model, so it may be possible. I have very strong doubts, though.
Mainstream laptops, especially, have virtually no upgrade path for CPU's because of the BIOS not being able to support more than a few CPU's (at the most), but since the i7-2670qm was at least in a recent DV6 model, it has a chance. It all depends on if they have the same motherboard.
My gut feeling is that you're stuck with the i5, but if you want to try it, I suppose you're more than welcome.
My internet speed is 10mbps down and 3mbps up.
However, I believe the modem and wireless router are outdated, I can't watch Netflix and play games (without streaming). So I might have to bump my speed up if I wish to do that.
Thank you everyone who has answered, I will look into the cpu's that have been listed here.
From what I can tell, as long as the motherboard has a socket, it should be physically compatible (looks like the same socket for the i5 and i7. PGA988).
I'm more worried about the BIOS being able to recognize it, though, and there's really no way to know that until you try it, unless you find some concrete evidence that someone has done it successfully (since there doesn't appear to be an actual list of supported CPU's for that model).