Initially it struggled to survive a single day and it was only after a lot of Apollo 13 style "Shut it all down!" that I managed to get a more reasonable 3 to 4 days until reaching 15% left.
As part of this blog's public service tech support, here's how:
1. Turn the screen brightness down. The screen might be lovely but it eats a lot of juice so set the brightness at a minimum (Settings->Display)
2. Turn off Google Play updates. You don't need the latest app update immediately, and you don't even need to know that an update is available. So save yourself a lot of power and only update when you have both wifi and
3. Switch off Google Now. I was preparing to leave to meet a friend for lunch when I got an alert saying it was time to go (which I obviously knew already). It was pretty smart and accurate but then I didn't need that message and to generate it there must have been all sorts of processing including requesting travel times off London Transport and location fixes which drains the battery. Clever but not worth risking an empty battery for
4. Switch off location services. GPS really does take a lot of power and you know where you are (its called "here"). If you are really lost (i.e. don't know where "here" is) then at that point switch in on but until then save the battery for when you really need it (Settings->Location)
5. Switch off Auto-Sync. Do you really need to know right now that an email is waiting for you? Surely its better to take control of your inbox and check it at a time that suits you rather than being a slave to the notification flashing light and save battery at the same time (Settings->Data Usage->Settings menu->Auto-Sync data)
6. Switch off various apps sync features such as, for example, Facebook updates. I'm pretty sure that photo of a baby with a cat can wait to be seen (Facebook->App->update)
7. Don't play graphics intensive games or watch videos. Yes I know the Nexus 5 can double up as a games console and video player but the battery simply isn't sized for those applications.
If you want the phone to still be working after a few days then "only" do the standard email / web / news / camera / photos / travel / weather / facebook / twitter / texts / phone calls / evernotes / ebooks (limited) / wikipedia / music player (downloaded not streaming) / alarm clock / solitaire / calculator / contacts / calendar etc.
You could also reboot to make sure all those settings are fixed and clear out any unwanted processes.
It probably helped that I live & work in areas with good LTE signal as the battery dropped a lot when I took the tube a couple of times.
I don't think the answer is replaceable batteries as who wants to spent their time carrying spare batteries? The answer must for handset manufacturers to install larger batteries - at least 50% bigger than the one in the Nexus 5 and preferably twice the size.