The iPhone 5 was only released 2 years ago (21 Sept 2012), yours can't possibly be 2.5 years old.

Ok, apparently I have a 4S. Maybe it's older than I thought.

I know someone with a 4S and the battery really struggles now especially when using GPS.

This happened to me. I bought a Mophie Juicepack for it and it solved the problem...by doubling the weight/volume of the phone.

Got an iPhone 6 on friday.

Yesterday I went on a 2.5 hour, 30 mile bike ride, and the iphone6 battery meter was essentially still at 100%. My 4s would have been well under 50%. Of course, the M8 is why, but after 3 years of recharging the 4s every night the battery was really starting to feel it.

Mine is the same age. Note I haven't measured but but hour plus browsing sessions have a fairly negligible impact on the battery so I'm confident it would at least reach about 5 hours (in percentage terms closer to 10 hours than 1-2).

When browsing on weak LTE the situation is different and 1-2 hours sounds very plausible. Maps/navigation can take big chunks out of the battery in a period of an hour or two and I need +60% before I set out on a 3 hour bike ride with Cyclemeter on.

Early iphone 5 units had a bad run of batteries. There is a free replacement program. Apple has a web site to check your serial number to see if your phone is afflicted. It made a world of difference on mine.

If your phone has had 2+ years of continuous use, you have definitely lost battery capacity. It does happen gradually.