You posted here with Firefox 53.

Firefox 54 was released on 2017-06-13 - 8 days ago, so that is a legitimate message.

blackcar said

When I turn on my computer using windows 10 and click on a desktop icon I get a prompt to update Firefox. Is this a legitimate prompt from Firefox?

Depends on whether or not you have set Firefox updates to automatically be installed. To make sure, would you check this, please :

3-bar menu => Options => Advanced => Update tab

Under   'Firefox Updates',   have you checked : 'Automatically install updates'   ?