Grouping data by timestamp and interval

Someone asked today on irc about grouping data, that contains timestamps, into “partitions".

Usually when someone wants something like this, you can do grouping by date_trunc(), but this time, this person, wanted to group data that all timestamps are within given interval from each other.

I'm not sure I understood him/her right, but I think he/she wanted something like this:

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Grouping data into time ranges

Today some guy on IRC asked question, which I didn't fully understand, but which could (probably) be summarized: how to group data into 5 minute intervals, based on some timestamp column.

Well, it seems trivial (as long as you know how to do it), but since he clearly didn't know how to do it (or I misunderstood his problem), here's the explanation:

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