Thanks for encouraging my OCD.
I'll bet you got your unimpressive score using a wifi connection? Am I correct?
Ok, testing my IP5 on browsermark brought out something curious, a wifi issue with the ip5 that many people are aware of.
I have 2 iPhone 5's in the house, and a 4s.
The first thing I noticed was, my 5 on a fast 32-34 Mbps wifi connection didn't score well like yours didn't. Anywhere from 1475 to my best of 2000, most were in the 1500 area, admittedly pretty crappy since the 5 is supposed to get closer to 2500. Here's the thing...
I turned wifi off and did the tests with my much slower att "4g" hspa connection (NOT LTE), which typically is about 4-5 Mbps, compared to my much faster 33 Mbps wifi connection.
Sure enough, the same phone scored 2500-2600 on my much slower 3G connection. Turn wifi back on, much worse scores, despite the fact that my wifi connection will consistently score 33-34 Mbps and 17-20 ms ping times.
I bet if you do the test again, but not with wifi, you'll get closer to 2500.
There's something wrong with wifi on many 5's, not all it seems but many, 6.0.1 didn't fix it. Some speculate its a bad batch of wifi chips that allow wifi to work, but not have the sort of throughput it should. Which is why there are many reports of very slow downloads over wifi, excessive youtube buffering where turning wifi off actually makes it faster, etc. there's a 150 PAGE thread on apples website forum about screwy wifi on the 5. And other smaller but similar threads there too, as well as several here.
This odd browsermark performance where a 33 Mbps wifi connection turns in a horrible score, but a far slower 5-6 Mbps 3G connection turns in a top notch score, is IMO another indication that there are issues with the 5's wifi, whether its hardware or software, I don't know.
To the OP, do a retest on a cellular connection, if your LTE is weak, turn it off and use good old hspa+, I did, and my score went from 1475 to 2600. Interesting...