I was just trying to put some new music on my iPhone 4 (just temp phone until Christmas), I have had it for around 5 months, after losing my old iPhone 4s 6 months ago. I thought the backup was for music so I tried backing it up, clicked the wrong one and it backed up my OLDER iPhone 3GS from almost 2 years ago. So now everything I have had for the last 5 months is gone, since I have never plugged this one into iTunes before or backed it up is there any way of getting it back?
So, I don't think this is necessarily as simple as the current answers make it out to be.
Technically no, if you don't have a recent backup, you can't restore your phone to it's most recent state.
However... a backup (in its simplest form) is just: - a list of apps you have installed, and where you have them on your screen - your email / iOS settings - any data stored in the apps - photos (unless you have iCloud photo enabled, then photos are not part of the standard backup)
So, given the above... music is not part of a backup. Any music you've purchased through iTunes is already part of your account. You just need to download it again (it's already paid for). Any apps you've downloaded can be downloaded again as well... they are already purchased. If you aren't using iCloud photos, you might lose some recent pictures taken... but that's going to be about it.
Almost everything done on an iPhone is easily recoverable without a "backup". The backup just makes things easier.
Like Tetsujin said, no, sorry. Only if you have another backup or if it was set to backup to iCloud.