Проблема на сервере, Too many connections

Looking for an experienced Linux System Administrator / DevOps to diagnose the causes of periodic crashes of the online store. It is necessary not to temporarily eliminate the symptoms, but to find the root cause of the problem, explain it, and propose an optimal solution.What is known The online store has been operating for over 15 years. Linux server. PHP 5.6. MySQL. OPcache is enabled. SSH access is available. Access to the hosting panel is available. Access to logs is available. Server load graphs have been added.Symptoms Periodically: the site stops opening; errors occur: 503 Service Unavailable; HTTP 508; Client.Timeout exceeded while awaiting headers; the response time of the site sometimes increases to 8–11 seconds. Sharp peaks in CPU, memory, and Entry Processes are observed in the load graphs. No critical errors were found in the available PHP logs.Required to conduct a full diagnosis; to find the root cause of the problem; to identify the bottleneck; to explain the cause of the crashes; to propose an optimal way to eliminate it; to perform the necessary work after approval.Mandatory experience Linux; SSH; Apache / Nginx / OpenLiteSpeed; PHP; MySQL; server performance optimization; finding the causes of periodic crashes and high load.Before starting work, please answer How many years have you worked with Linux servers? Have you had experience in finding similar problems? What tools do you plan to use for diagnosis? Have you worked with old PHP projects (PHP 5.x)? What is the cost of the initial diagnosis? What is your hourly rate for further work (if needed)? When can you start? Please do not send template proposals. In your response, briefly describe what you will check first. If the problem is successfully identified and resolved, I am ready for long-term cooperation in server administration and development.