What sort of person says "only 5 or 10 minutes of fuel left" on a PA? Doesn't matter if they meant 5 minutes before needing to divert and land with reserves, it's a stupid and aggravating statement.
If I'm going to give a reason for diverting it'll be along the lines of "unknown delay", "airspace closed", "weather", or "ATC told us to".
Many of my colleagues seem blissfully unaware that a sizable proportion of our passengers hate flying with a vengeance and talking about fuel (specifically the lack of it) is insensitive in the extreme to someone who's already nervous.