You are fine. The 5 qt. limit is minimum for take-off. Basically, Lycoming and Cessna believe that at 5 qt., you'll run out of fuel before you run low of oil. The reality is that most of the oil in the pan is for cooling, not lubrication. As little as a quart or two will lubricate the engine. I believe (someone check me on this), the engine is actually rated to run all the way down three quarts, even from a cooling perspective.
Also note that the engine actually has an additional quart you don't see on the stick, as the stick is calibrated for no oil filter, and all IO-360-L2A have oil filters. That doesn't help for the level, as you need the extra oil to fill the filter. However, that extra oil does increase the cooling capacity available.
I personally use 6 as a minimum as well, but there's nothing that is really wrong with using the book numbers. Also, even the book indicates that most of the last quart, the eight quart, would be wasted out the tailpipe if present. That last quart is really only there for long, hot trips on a tired, oil-burning motor.