Need a little more info, like the Brand & Model number of the laptop.
There are a couple of schools of thought on this kind of thing for a laptop especially. Your machine was designed around a core. Without knowing what your model is I can only guess...but many wouldn't work any better with a core upgrade. I also see the i5 (quad core) uses a different socket then the i3. Your mobo manufacturer will have a listing of which cores it will support. A dual core i5 is around the same capability as your i3, if there is even a dual core i5 that would fit your socket.
Many people that have a slowdown or sluggishness (BTW, how long have you had the laptop, and if it's branded, how much of the bloatware that comes with a branded computer is still running?) drop back to XP SP3. Others I have worked on have so many accidentally loaded resource hogs that just removing all the supposed 'help bars' from their internet browser speeds things up. These days, you must always choose 'custom' install while installing software you actually want in order to turn of the hidden bars (which still run, even if the browser is shut down) which often are installed during the 'Standard' or 'Default' install. The Ask tool bar is often installed this way. So are all the resource hog 'Google' helper toolbars. Then of course are the malware bars, spambots, commercial bloatware (HP has been doing this for years - and many times their printers won't work unless their bloatware is running, always connected to the net...the worst kind of corporate intrusion).
So, perhaps taking it to your friendly neighborhood consultant would be of benefit.