There are 3 major difference between processors, core count(dual quad hex), speed(usually GHz), and archtecture(i5-7xx, i7-9xx, i7-2600, etc)
In general, its pretty difficult to make a direct comparison between them based on specs alone, but one thing you can know is that the newer Core ix series is better clock for clock than the older Core 2 line up, so a C2D @ 2.66 will lose to an i3 @ 2.66.
There are a lot of Core i5 processors, some are true quads some are hyper threaded dual cores so which i5 are you looking at in particular? It is likely at least slightly quicker than the Core 2 Duo in dual threaded tasks, and in four threaded tasks it will be significantly faster regardless of if its hyper threaded or a true quad, but the true quad would be significantly faster than the hyper threaded dual core in those tasks.