Yes, you should certainly try the secure server, add it to Alt.Binz as a new primary (deselect the others), check the SSL box and make sure that port is 443 or 563. You should also raise Number of Connections to see if you get better speeds (maximum for Astraweb is 20).
With a 5Mbit connection, you should be getting around 600 KB/s (5000 / 8) speed, so if the above doesn't work you should do some trouble-shooting:
1) Switch off firewall and any antivirus temporarily (check also whether NNTP traffic is scanned)
2) Open command prompt, type: tracert news.astraweb.com
This should tell you if there are any network problems.
3) Check your ISP's fair usage policy - some simply throttle all connections regardless if usage in peak time is over a certain amount. So try at different times of the day.