Core i3 and core i5 processors. What is the difference? What do I choose?

Background

i3 is an Intel "low-end" processor range.
i5 is an Intel "mid-range" processor range.
i7 is an Intel "high-performance" processor range.

Generally speaking, the i7 is better (faster, more cache), then i5 and the i3 being "worst" (slower, less cache), but obviously the cost scales as well.

Some Wikipedia links you might find useful regarding these ranges: Core i3, Core i5, Core i7.

Answer

If you're interested in high-end games, remember that your GPU (Graphics card/adapter/etc) will be vitally important as well, as will having a reasonable amount of RAM. Having a massively powerful CPU will not help if your GPU is poor - you will still receive relatively poor gaming performance.

Using CS5 and some multimedia tools also leans me towards saying that you ensure you have a good quantity of RAM as well - these types of software can consume a lot of memory when running, and if you have insufficient RAM and they have to start using the page file then performance will be poor.

In summary, having an i5 over and i3 might help, it might not - it depends on the rest of the machine in question (you need to identify the weakest component - the performance bottleneck - and improve that for the best overall improvement).