You have a few questions combined here so ill break them down.
How to tell the space available on your HDD's
1. Select the Apple menu () > About This Mac > Then click the Storage tab on the top of the box that appears.This will give you a visual run down of the used and unused spaces on connected HDD's
2. Disk Utilities, will give visual and text information on your connected HDD's
You can access this via Spotlight, Applications(Utilities Folder), or Launchpad(Other Folder) etc.
Your primary concern seems to be more about the backups.
First of all, like any hardware HDD's have a lifespan. Five years is a good run, and you may even get another five or even more. But it would also be wise to start considering additional back up solutions. Assuming you are using Time Machine (Built in back up application) you can have more than one HDD backing up at any one time.
Time Machine
Time Machine automatically makes hourly backups for the past 24 hours, daily backups for the past month, and weekly backups for all previous months. The oldest backups are deleted when your backup drive is full. So in theory if your HDD is full it should not be a concern.
If you have it enabled you can click the Time Machine icon in the menu bar on your Mac and in a faded text it should tell you when the last back up was performed if it was recent you should have nothing to worry about.
If you do not have the icon in your menu bar, choose the Apple menu () > System Preferences, then click Time Machine.
Time Machine will only back up the changes on your mac so you can revert or recover them as required, if your mac is sitting on idle for 2 days do not expect it to perform hourly back ups during that time.
Getting back up errors? you can refer to If you can't back up or restore your Mac using Time Machine - Apple Support of Contact Apple for support and service - Apple Support