i7 has more cache than the i5, so it can not only repeat repetitive commands faster(think spreadsheets and databases), but that extra cache allows for more background programs & processes to be stored and brought to the forefront more quickly when you switch between multiple programs that are running.
An i7 also has hyperthreading, so while both an i5 and an i7 have 4 or 6 physical cores, an i7 has an equal amount of "virtual" cores as well, so Windows will handle a 4-core i7 like it has 8 cores, and it will multitask a lot better if you are using a program that benefits from multiple cores (video processing/encoding, rendering, etc)
So, if all you're doing is gaming, and i5 is fine because very few games take advantage of multiple cores, but theres definitely a lot you can do with a PC that would use those extra cores/hyperthreading.