Not the timing belt, which would show up as the engine giving more-or-less
normal cranking sounds (maybe faster, but certainly stopping when you
release the starter) but no firing.
Nothing comes to mind... it will help if you can determine whether a
particular fan is running loudly or if the sound could be coming from the
pump in the gas tank, or from the engine itself (which would suggest the
starter is spinning but not engaging - don't know why it would continue for
5 minutes, though).

(Presuming the sound isn't coming from the starter...) Quick and easy to
try - if it is an automatic, see if it will crank when the gearshift is in
Neutral. The safety switch on the gearshift will prevent the engine from
cranking, and the switch may not be working in "Park" now.

If the sound is coming from the starter, it has to be a stuck solenoid.
There is a bulge on the side of the starter that houses the solenoid. A
modest whack with a hammer (like cracking a walnut, but use less bounce)
often frees the solenoid, but if that gets it working now it only tells you
the solenoid is actually jamming. DIYers usually clean and relubricate the
solenoid, but professionals prefer to replace the starter to limit their
responsibility in the event the problem returns. Rebuilt starters (and
alternators) have earned a bad reputation for reliability, and genuine Acura
starters are expensive. Kind of a devil's choice if it comes to that.

Mike

Sounds like a worn out battery that won't turn over the engine but will run
electrical components.  Try jumping it.

Doug