Depreciated PHP mysql connect error

I have two websites that are using a legacy version of PHP and as a result, are now both down and showing service 505 errors. Both websites use a depreciated mysql extension and I need someone who has experience in fixing this issue so that both websites become operational again.

https://exmoorfarmselfcatering.co.uk/
https://exmoorworkingdogcoats.co.uk/

I have attached a txt file that contains the error log and an example of the current db connection php file so you can see.

I can get you access to my cpanel.