I don’t think anyone can give you a guarantee that you will have no problems, however typically WordPress handles the upgrade process very well. You are only a couple of versions behind so I wouldn’t anticipate any major problems.
You should consider:
- Back up all the files and database before proceeding. If you don’t know how to do this, ask your web host about what backup services they can provide.
- Test the upgrade if at all possible. Restore to another area of your server and give it a go, this is the only way to be sure.
- Look at the plugins you have installed and check that they are all compatible with the latest version of WordPress. This information will be available on the plugin’s page on WordPress.org.
That’s probably all you can realistically do to mitigate any problems. Like I said at the start, it should work OK, but it pays to be cautious if you can’t afford to lose the site. Regular backups should be part of everyone’s site maintenance routine anyway.