Pin 6 has a mean value of 2.24V, but from looking at the signal, it's a square wave that spends roughly half its time high and half it's time low (50% duty cycle) so that mean of 2.24V will be about half-way inbetween those high and low values. It has a peak-to-peak measurement of 5.28V; the low is ~5V lower than the high, which is good! And because the duty cycle is around 50%, we can halve the 5.28V peak-to-peak reading, and add/subtract it from the mean to estimate the high and low values.
Doing that gives high and low values of roughly 0V and 5V. So I'm not concerned about the values on pin 6.
The mean and peak values for pin 5 are off, though. That nice square wave is labelled on the diagram as 2MHZE, and should be a 2MHz clock signal that goes to good clean high and low voltages like pin 6. I suspect that you may have knocked the 10x switch again when measuring that pin.
If pin 5 actually measures a clock signal oscillating between 0V and 5V, I'd be happy with the behaviour of that gate. Pin 4 is high most of the time, and while that's the case the NAND gate will effectively invert the value of pin 5 to get the output value for pin 6. Pin 5 is high ~half the time, and so is pin 6.
Note that because you've measured each pin independently (with a single probe) that the horizontal timings aren't synchronised. So it's not unusual that pin 5's high periods coincide with pin 6's.
Your scope may have other dials or knobs to let you measure the voltage at any particular point on the waveform, or describe the scale of the background grid. Have an explore and see what you can find.