Ideally when the input if +6V that would be an ON state and +5V would be OFF.
Ok. A comparator with a 5.5V threshold would do. I don't know what the power supplies are in your system. What is VCC? (5V? 3.3V?)
If you don't want to bother with power supplies, instead of going higher, you'd just have to attenuate the input voltage so that 5.5V gives for instance half-way VCC? Set your threshold voltage accordingly.
(Eg: a resistor divider that divides by 2. 5V will give 2.5V, 6V will give 3V. A second resistor divider - but from VCC - to generate the 5.5/2 = 2.75V threshold.)
Take care of the operating range and working supply voltage of the comparator or opamp you're going to select. Power it at VCC.
You can also do the same but add some hysteresis to your comparator (so for instance use two thresholds such as 5.25V and 5.75V) to avoid spurious toggling if the input signal is a bit noisy and/or could be too close to the middle voltage (5.5V).