Air carrier flight crew reported they had a near midair collision with a hang glider during descent into AUS.

Narrative

On the SEWZY6 Arrival while in contact with Austin Approach; we were descending between 5;000 and 6;000 feet between VADRR and MGTEC. I was looking to my left and the FO was checking the MCDU (Multipurpose Control Display Unit) when our jump seat occupant tapped my shoulder and directed our attention out the front window. At approximately 11'oclock; at our altitude was a HANGLIDER coming straight at us. I initially reached to take evasive action but judged that we would cross in front of him without making contact and that an abrupt maneuver could cause injury to the FAs that were likely still doing their final walkthrough. The HANGLIDER passed off our left wing at our altitude at a distance of what is estimated to be about 100 yards. We advised ATC and continued the arrival into AUS with no further incidents. I followed up with calls about the incident to ATC; Dispatch; and a safety organization.Cause: Non-radar traffic flying on and in the vicinity of major commercial aircraft arrivals and little to no warning of their presence.