As mentioned previously I tried to install Android 5.0.2 in VirtualBox and failed, and then found the source project Android-x86 - Porting Android to x86 where I retrieved their Android 5.1-rc1 ISO. This installed flawlessly and incredibly quickly: the interface is responsive and everything (so far: not tested extensively) works exactly as expected. My only issue with it is that during installation I had to set VirtualBox's mouse settings to "USB Tablet" because "PS/2 Mouse" wouldn't work at all. The "USB Tablet" behaviour is pretty awful, but got me through the install. After a reboot, "PS/2 Mouse" worked fine and is preferable.
Update
I don't appear to be able to install any applications from the Google Play Store - it tries to download them and nothing happens. Since I mostly wanted this for messing about with Apps, this is kind of limiting.
I used a variable-size virtual hard drive: the one for Android 4.3, even after some use, is around 800MB. The one for Android 5.1 is 3.3GB right after the install.
See Also
- Getting Android Running in VirtualBox (Android version 4.3, now a bit outdated)