Hi… Try posting your full fly.toml along with the output of fly ips list and fly services list. You can use the </> button in the toolbar to get an area suitable for pasting code and outputs, without them getting interpreted as style formatting, etc.
Generally, problems like this are due to missing handlers or to not having a dedicated IPv4 address.
Given this stanza, the right way to connect is https://df-eng-wispy-wildflower-1123.fly.dev/process, i.e., leaving out the :5000 that you had been inserting into the URL.
Like @lillian said, the Fly Proxy in the middle will forward port 443, incoming from the public Internet, to port 5000 within your Machine.
If you encounter 502 errors when attempting that, do fly logs -a df-eng-wispy-wildflower-1123 in a terminal—and leave that running while you try the URL again. Typically, there will be messages in the logs about what went wrong within the Machine…