No.

You should always follow manufacturer's recommendations. However, the
manufacturer may not include all of the information about oil choices
in the owner's manual, so you may want to check with a dealer. The
dealer will have more extensive information about oil choices that, I
bet, include the conditions under which 10W 30 oil might be a better
choice (high temperature, severe service, etc.).

As a general rule, the lower viscosity oils give slightly better fuel
mileage. Honda engines regularly clock over 200K miles with
appropriate care, so 80K may not be a "high mileage" engine. Modern
oils are so good that there is little reason to change based on age of
the engine. Assuming high quality oil. (And, for what ever it's worth,
every mechanic I know uses Castrol GTX in their own car. That's also
what my Honda dealer uses at oil changes.))

On the other hand, as far as I know, there would be no problem
substituting 10W 30 for 5W 30, especially if the ambient air
temperature is high enough, as for example right now in Austin, Texas,
where we are flirting with 100 degree days.

It is my understanding that 10W 40 oils should not be used under any
circumstances. To get that large viscosity range, oil manufacturers
have to add "viscosity improvers." These are various polymers that
stay balled up at low temperature but unwind and tangle together at
high temperature. When they tangle together, that raises the viscosity
of the oil. If that sounds like it might be bad for your engine, you
should know that experts also think it might be bad.

Anyway, that's what I was told.

Elliot Richmond
Freelance Science Writer and Editor

 Who do you believe?  The engineer from Honda or a simple
technician?  To have credibility, the tech better have science
facts to support his speculation.  No solid facts neither
based upon science nor supported by numbers?  Then he is
probably promoting junk science.

 This is not just how one selects motor oil.  Some are so
foolish as to believe the junk science reasoning from
mouthwash manufacturer such as Listerene and Scope.  If their
reasoning was correct, then Vodka is a better mouthwash and is
superior to a tooth brush with fluoride toothpaste.  Where is
the science that says mouthwash is so effective?  Same
mythological reasoning.

 Consult Honda.  If the tech says otherwise then hold his
feet to the fire.  Either he will provide those facts (an
honest man) or he will get emotional (symptoms of a myth
purveyor).

Your technician is wrong.  This was a standard practice many years ago
when engines were constructed to loose clearances.

The engine has small passages to distribute oil to where lubrication is
required.  These oil passages have been sized to distribute oil flow
approriately with the correct weight oil.  If you use a thicker oil, the
oil will flow through the smaller passages slower, thus providing less
or no protection.  This will especially be a problem on cold start.

Use the manufacturers recommended oil weight.  A synthetic such as mobil
1 or amsoil of the correct weight will extend your motor's life.

Also, change the oil (and filter) at 3000 miles.  Extended oil changes
are poor economy because engines are much more expensive than oil.