I dont have the original tunes in my SCT, I have the Innovative package, so the power output might be a little different. I tow on the tow tune, but I am towing 18000.
Towing 5000# I would not worry towing on the street tune. It all will depend on your right foot and the terrain. If it is relatively flat, dont worry about it.
If it is really hilly, then I would pay attention to the gauges. On the tow tune, up 7%+ grades I can hold the speed limit (55 in CA) and the EGT's are 1250 and down. The 6.4's run much cooler than the 6.0 do towing when tuned. My 6.0 on Innovative's tow tune, I could get to 1250 easily.