There are 3 possibel resolutions to your issue.
If your cable company offers a different model of cable box that incorporates a component video and audio output set; then have them swap you out and your good to go.
This method gives you max resolution of upto 1080i on the TV as well as the slingbox.
If your cable company truely only has box's that incoporate only HDMI out; then only options 3 and 4 will solve your delema.
Purchase a 1x2 hdmi switch. The switch connects to the hdmi output from your cable box and gives you 2 identical hdmi output feeds. 1 of those feeds gets connected to your TV's hdmi input for normal operation, while the other hdmi output feeds gets connected to a HDFury 3 adapter cable (which converts hdmi to component video and audio). The resulting component feeds get connected to the component input for video and audio on your slingbox.
This method will give you upto 1080P on the TV and 1080i on the slingbox.
Same as above; however you don't need to purchase the 1x2 hdmi switcher. Simply buy the HDFury 3 adapter cable. Out of the adapter cable to the slingbox's component video and audio inputs; then out of the slingbox's passthru component video and audio outputs to the tv's component video and audio inputs.
This method, although cheaper, will give you a max resolution of 1080i on both the TV and the slingbox.