Website speed and performance

We have a website that was handed over to us due to some performace issues. We have changed the theme and updated some of the sites plugins andcleaned the databases however we are are still getting some error 500 and error 503 when running any website speed checks. Need help solving this issue. We believe there may be some old files in the file manager that may be causing this problem. We currently have the site in maintence mode while we complete the changes
duo21.mx