Just for laughs, check the external IP of your Netgear...make sure it's a public address. That'll let you know if you've got bridge mode set or not. If the external address (WAN) of your Netgear is a private IP that would indicate the DSL modem is still in router/gateway mode. FWIW, I can set both my DSL modem and my Linksys in router/gateway mode and access the Internet, but port forwarding becomes an issue.

The port should not be blocked at any time if you've got it opened up. If you're doing a scan of your router (from the external side) you should absolutely see 5001 open...without that, you're not going to be able to watch the Sling from outside your network.

I'm still leaning towards your DSL modem not being in bridge mode. Not trying to be stubborn, but if you've got port forwarding set up on the router (it's pretty straightforward) then that's the most likely problem. And if you can access the DSL modem's admin pages, that's also typically a good sign that it's not in bridge mode.