Heyo go_hercules
The only thing I've seen where the i3 might be faster than the i5, is when comparing something like an i5 6400 and the i3 6100.
The people you've seen writting that the i3 is faster in some intances, might have been refering to a lower end model of the i5's. The reason why they have done that, is since i5's have their true 4 cores and the i3 'only' has its 2 cores with hyperthreading, and since hyperthreading is basically making 1 CPU core into 2, but then again not, since it's just making its scheduling more effective. This make the i3 almost as fast as the 4 true cores in the i5.
Hyperthreading can make a 2 core CPU act like 4 core, but hyperthreading is NEVER as good as a true core.
In your case, you should probably look at the i5 model and make sure that its clock speed isn't too low, since the i3 otherwise would beat it in some cases. Could you link the PC's you've been looking at?
Hope this was enough answer, and good luck buying the pc!