You can only connect up to what your internet service connection goes to. The website your connecting to also has to support that speed. Just for example, if you try to stream movies from JoeBlowMovies.com and his site only has a 10mbps connection, then that's what you'd connect at.
The key to the statement you originally said was "up to" 50 mbps - I would suggest that you very rarely actually achieve this speed. Your router Hub is probably set to 10 Mb/s unless - check how fast your network card connects to this first.
Your computer will transmit at a maximum of 100 Mbs when communicating on the local network.
All internet connections will run at the maximum speed of your internet connection, which is 50Mbs or whatever your upload speed is.
Now keep in mind you will never get those speeds on a consistent basis. Maybe burst, but not continuous due to overhead in the network traffic.
Also connecting to the internet at 50Mbs does not really mean much - you may get that speed to your ISP in bursts (as Sturm says) - but you wont get that to Youtube, Facebook etc - as you will be sharing the ISP's pipe out of their data centre etc etc round the web to the target server... Check out tracert command in DOS to see how the hops work. Some will be quick - some slow.