Your website is lying to you

Joomla 3.2.7 was released Oct. 1 2014, and was already antiquated at that time because the Joomla 3.3.x stream had launched 5 months earlier.
As of this week, latest version of Joomla is 3.9.11. The good news is that upgrading within the 3.x realm is often pretty smooth.
Some upgrade tips:
- Check your most important extensions to ensure that they will run in a Joomla 3.9 environment.
- Check that your template is compatible with v3.9 Joomla
- Joomla now recommends PHP7.1+, but (for now) will still run on PHP5.3.10+ . Does you're host allow you the option to change to 7.1 or higher? Do your extensions support PHP7.1+? See the Joomla technical requirements at
downloads.joomla.org/technical-requirements
.
- Make a backup of your website and database, either manually or install & use Akeeba Backup. You may wish to test-recover your backup on a localhost or other server to make sure it is reliable!
- Download & install the latest version of Joomla from
downloads.joomla.org/cms/joomla3
. Pray that all goes well, and that your extensions and template don't break. Restore from your backup is things go bad

If using Akeeba Backup, familiarize yourself at least a little with Akeeba Kickstart before upgrading, just in case you need to do an emergency restore (Kickstart is their backup restoration app).