I have a MacBook Air 13" and I would like to upgrade to OS Sierra I only have 5 GB of storage and I have already installed the installer but how much storage do I need on the HD to install it on there?
15 gb of free space is my general rule for starting an upgrade. However, if you can free more, that’s always better. Since you have the installer, you can deduct that from my 15 gb figure. 

Also, be sure you have a solid backup and maybe even test it before you install if you know you are potentially going to run out of working space as the installer runs, migrates all apps and settings and then cleans up old and temporary files.