No because HDMI is digital and your TV has analog connections. Since your cable box only has 5.1 I would just use a simple optical cable. Save the HDMI for a Bluray player. Your reciever should have component inputs, so I would use component from your cable box and an optical cable to the reciever for audio and then component to the TV, (hence using your reciever as a switcher if you add more devices.
I currently have an HD-DVD, Bluray, Oppo 970 DVD player and Directv HD box all going thorugh my Onkyo 805. I use HDMI for my HD-DVD and Bluray to take advantage of the lossless audio but have all video sources going via component (three to the Onkyo and the Oppo directly to input two on the back of my 58" RPTV without DVI/HDMI.
Some of you may wonder why I use the Oppo, it's because I have one that can "upconvert to HD" via component cables. The 970 somehow was one of two DVD players that could achieve this.
But to answer your question, no you will never get HDMI to output an analog signal.