Deprecated: mysql_connect()

I’ve just set up a brand-new vanilla instance of WP 4.4.2 on a cPanel account, using the default twentysixteen theme, no plugins installed beyond the default, nothing extra whatsoever. Because I am going to be doing a bit of work on it, I enabled debugging in wp-config. I got three errors, one of which was this:

Deprecated: mysql_connect(): The mysql extension is deprecated and will be removed in the future: use mysqli or PDO instead in /home/[directoryname]/public_html/wp-includes/wp-db.php on line 1518

My current PHP version on my server, which I run myself, is 5.6.13. Do I need to downgrade PHP versions to get rid of this error? Do I need to worry about it?

For what it’s worth, I’m getting two more errors as well:

Warning: Cannot modify header information - headers already sent by (output started at /home/[directoryname]/public_html/wp-includes/wp-db.php:1518) in /home/[directoryname]/public_html/wp-includes/option.php on line 820

Warning: Cannot modify header information - headers already sent by (output started at /home/[directoryname]/public_html/wp-includes/wp-db.php:1518) in /home/[directoryname]/public_html/wp-includes/option.php on line 821