I can answer your question. In terms of CPU utilization, there are three kinds of programs the average computer user will encounter:
- Programs that don't use very much CPU at all (most programs)
- Programs that use only one thread of a CPU heavily (a few programs)
- Programs that use all threads of a CPU heavily/evenly (a few programs)
So what does that mean for you? It means that for everyday usage, you will see absolutely no difference between the i3 and the i5 in question. While the i3 does indeed have a higher single thread score than the i5 - and suffers from two fewer cores - it uses hyperthreading, so in fact it has four threads it can execute programs on simultaneously, the same as the i5. I'm not going to get into why hyperthreaded threads are not as desirable as fully physical threads here, but suffice it to say this is kind of like a middle ground between a true dual core and a true quad core when it comes to multithreaded performance.
So what programs will actually see a benefit from that i3's higher single thread performance, anyway? The answer for most users is precious few. Older computer games, some parts of photo editing software performance, a few OS operations... I really can't think of anything else. There are lots of programs that are still single-threaded, it's just that most of them fall into category 1 - you won't see ANY benefit past the point of, say, a Pentium 4 @ 3.4ghz!
On the other hand, what programs will see benefits from the full four cores of the i5? Again, the answer for most users is precious few. The OS itself sometimes uses all four threads heavily, zipping/unzipping files is often a heavily multithreaded process, and watching HTML5 video or webms can sometimes see fairly high multicore utilization, especially if more than one plays at a time... but (and this is another wrinkle to the answer) since both of these CPUs in question feature GPUs with Intel's Quicksync video encoding technology built-in, handling some of the most demanding multithread CPU work a modern user might commonly encounter, having to do with HD video playback, encoding, etc - there will be much less of a difference between the two processors than the simple multithreaded benchmark score would intuitively seem to indicate.
The one caveat to all of this is that if you are a true multitasker - if you have more than one demanding task going at any given time - the i5 is probably going to be a better bet for you. For example, if you wanted to zip a large file while simultaneously transcoding media being cast to your TV and using a word processor on a large document - that might warrant the more powerful CPU.
For the average daily user who simply wants to listen to music while watching a youtube video with about 20-30 chrome tabs open in the background and maybe a torrent going - both of these CPUs are huge overkill. You could step all the way down to something like an A8-7600 or a Celeron G1840 without noticing much, if any, performance degradation. In fact, for the average daily user, something like the A8-7600, which can run at a 45W TDP and which sports superior integrated graphics, is probably a much better choice than either of these CPUs, because it is more efficient and sports a more balanced design (a good mix of single-thread, multi-thread, and GPU power).
Choosing between the two processors asked about, however, I'd have to recommend the i3-6320. It's cheaper, and since nothing else really stands out as being particularly great for the basic home user when it comes to the i5, there's no reason for me to suggest you buy it.