It's highly recommended to keep your website software (Joomla + extensions) up-to-date.
That way you prevent situations like these, or getting hacked because of some unpatched vulnerability.
To solve the current issue I would install a local webserver with PHP 5.6 (eg XAMPP).
In the admin panel of your webhost use phpMyAdmin to Export the database as MySQL.
On your local system use phpMyAdmin to import the MySQL database.
Use FTP to download all the files of your website to your local PC.
Put the files in your local webserver,
edit your configuration.php to reflect the changes (database settings, local logs + tmp path).
When your site is running locally, update all 3rd party extensions and upgrade Joomla to the latest version,
see
https://docs.joomla.org/Joomla_2.5_to_3 ... _Migration
When your website is working ok locally, create backup and install that on the server
I'd recommend to use Akeeba Backup to create the backup (of files + database) and use its kickstart.php to restore the backup on the server.
