Can (slow) Internet speed get you a 500 server error? [closed]

No. 500 error will return when you have server error. PHP error, etc. See response code reference.

The HyperText Transfer Protocol (HTTP) 500 Internal Server Error
server error response code indicates that the server encountered an
unexpected condition that prevented it from fulfilling the request.

This error response is a generic “catch-all” response. Sometimes,
server administrators log error responses like the 500 status code
with more details about the request to prevent the error from
happening again in the future.