Added: After more searching, I found How to remove the Google Search bar from your Android homescreen indicating you have these options:
- Disabling Google Now, which is not recommended on the Nexus 5 as it might soft-brick your device
- Install custom launcher, which you don't really want to do
- Using Xposed framework (root required), which doesn't seem to work as Exposed and ART is a bad combination
- Install a custom ROM, and then disable it
In other words, it seems like you need to make up your mind on either living with the Google Now search bar, installing a custom ROM, or install a custom launcher.
Original answer with fails
The 14 Essential Tweaks to Perform on Your New Nexus 5 Smartphone has the following to say on this topic:
You'll probably notice the search bar on the homescreen has a reminder to say "Ok Google" to trigger a voice search. It's a neat feature, but the text is a little annoying. It will go away only when you've proven you understand what it's saying. Just do any voice search from the homescreen to clear the text and get your nice, clean bar.
Fail 1: Does only remove the text, not the search bar
The previous tip is for the nexus 5 and lollipop, whilst the next tip is only for previous android version, from 25 Hidden Nexus 5 Features:
Open Google Now with the quick setting above, or swipe to the left and enter Google Now on the Nexus 5. Scroll to the bottom and tap the three dots on the bottom left (menu) > tap settings > and simply tap the On/Off switch at the top to disable Google Now.
Fail 2: Does only apply to previous version of Android
My final tip if none of the above works, I did the following on my Sony Xperia Z3 running Android lollipop:
- long press on home screen on an empty space
- toggle the hide/show button of the Google search bar
Fail 3: Correct procedure for some phones, but not for Nexus 5
Hope either one of these helps you out!