Only a tiny amount. I had Lollipop on my Nexus 5 for about three days before I got my Nexus 6. My 5 has now been sitting on a countertop, uncharged, feeling neglected.
In that brief period, it did feel like the phone was faster, but that could have all been in my head.
I like almost every aspect of Lollipop, but there's one change that Google has made in the name of material design that is absolutely, objectively bad: Google Calendar.
Seriously, I can't describe how badly they screwed up Google Calendar. First of all, there's a ridiculous amount of white space, which is somewhat OK on the gigantic Nexus 6, but on the 5 I basically had no information on my screen and I had to scroll all over the place. Granted, my complaints come mostly from the fact that I prefer the week view of the calendar, but even there they screwed it up and changed it to a "5-day" view. This, too, would be forgivable if it meant that there were more information about each appointment on the screen. But because of all the other space wasting design features, there's not! And to make matters worse, they removed the ability to pinch-to-zoom on the calendar, so I was seeing about 5-6 hours at most of each day.
I use the Calendar app for my business, so I can get a picture of my week and give clients my available times. Google's update has made the Calendar app useless.
I you're looking for a good alternative,
Today Calendar is fantastic. It has the material design of Google's new Calendar app, with the functionality (and more) of their old version!
*edit*
ps- sorry for the rant...