This really surprises me. Looking at the data sheets
for the Energizer AAA cells, alkaline E92 and lithium L92, the lithium clearly supplies a higher voltage at a 1000 mA drain and for longer than does the alkaline cell. The lithium AAA and AA cells are designed for higher drain applications than the alkalines are intended for.
Now 5 watts from 5 AAA cells would probably require something on the order of 1000 to 1500 mA, and maybe beyond 1000 mA the alkalines paradoxically start performing better than the lithiums, but that would be bizarre and intuitively unlikely. Energizer doesn't supply data for current draws greater than 1000 mA however.
Alkaline AAA data sheet: http://data.energizer.com/PDFs/E92.pdf
Lithium AAA data sheet: http://data.energizer.com/PDFs/l92.pdf
I would be curious to find out if this was just a bad battery
case or really reflective of what happens when lithium AAA cells are used in an HX851. I have an HX850 and will try the experiment
myself when I can restock on AAAs.