(note: none of the comments below answers your question, which I think is 5W-20 and I am sure will be corrected if wrong. But you may find it useful anyway)
2009 4.6 manual recommends API SJ, SL / ILSAC GF-3 or above and shows 10W-30 standard for zero and above temperatures, 5W-20/30 for below zero in the chart on page 8-5. It then states this:
1.For better fuel economy, it is recommended to use the engine oil of a viscosity grade SAE 5W- 20, 5W-30 (API SJ, SL / ILSAC GF-3 or above).However, if the engine oil is not available in your country, select the proper engine oil using the engine oil viscosity chart.
Some 2012 5.0s have oil burning issues (~1 qt every 1000-2000 miles), which I believe was caused by a) Hyundai using lower tension piston rings and b) lighter weight oils in the 5.0 engines to try and save on fuel economy. Many have been fixed by going to higher weight oil (from 5W-30 to 10W-30, pennzoil brand seemed to be a good one). A few have had engines replaced.
Big thread on the subject here:
http://genesisowners.com/hyundai-genesis-forum/showthread.php?t=10687