That’s exactly what a 503 is.
503 means that the server was relying on connecting some other service, which did not respond in time.
Server Error 5xx
Checked up on Wikipedia and the listing there seems to imply that a 504 would be the one I’m thinking of. Quite possibly the link over is outdated.
So:
504 Gateway Timeout
The server was acting as a gateway or
proxy and did not receive a timely
request from the downstream server.