QRP doesn't have a strict definition, though 5W or less seems to be a common threshold. So would "QRP operation" usually be considered to include UHF/VHF handhelds?
My personal opinion is that QRP means using significantly less power than is customary for a given mode of operation. In that sense, a 5W HT would not be QRP because pretty much everybody else with an HT is also operating at (or near) 5W. 0.5W might be considered QRP in this case.
My understanding of "QRP" is simply the use of as little power as possible to make contacts over interesting distances. There isn't a specific power level that equates to "QRP" - it is more a function of what's less than expected.
1W on 2m/UHF for 10 mile simplex (or local/regional repeater communications) isn't QRP. 0.1W on 2m/UHF for 250 mile simplex would fit my definition of QRP.
It is a gray area, for sure. Like the Judge said, "I know it when I see it."
Although it's highly opinionated, it may be defined as operating at 5% or less than standard 'barefoot' operating power on your band, by convention.
So, for most HF, 100W is the standard power, 5W is considered QRP.
For VHF, most handhelds (which are the most frequently used on that band) operate at 5W, so QRP would be 250mW.
Of course, that doesn't include whether you're counting power applied to your antenna system or your actual ERP :)
It's opinionated, and relative! QRP historically means "Should I reduce power?" or "Decrease Power"
I would say: No, a 5W handheld does not count as QRP, since that's well within the standard expectation for transmitter power for that band.
Please see: http://www.arrl.org/qrp-low-power-operating
While most 2m and UHF hand held units are limited to 5W, not all are (I have one that offers a choice of 1W, 4W, or 8W) -- and this is done mainly to extend battery life with a radio that's normally only useful for the distance to the nearest repeater.
However, 2m/UHF mobile units mounted in vehicles routinely emit 50W or more (I'm looking at a Yaesu for my car that offers 5W, 30W, or 65W, for under $150), and base units can readily emit 100W, or with an amplifier up to 1500W legal limit.
Hence, even though 5W is common for hand held VHF/UHF units, I still consider it QRP. A hand held could easily be built to radiate ten times this power -- though battery life would be compromised.