Depends on your Internet connection. 5GB in 3 hours comes to an average upload speed of 500KB/s. On most residential Internet connections, the upload speed is about 1/10th of the download speed.
You can verify your speeds by pausing the upload and running a test through
http://www.speedtest.net/. If your upload speed shows as 4Mb/s, this would come to 500KB/s, and therefore the upload speed would be consistent with your Internet connection.
If your upload speed is considerably faster, ensure you're on the latest OS. Restart your Mac with the 'reopen windows when logging back in' option unchecked. Restart your Internet router and try a PRAM reset on your Mac.