Well something is not level.

Either the bed is not level, falling away from the head, or the head is rising up.

And what do you mean by 5x? Is it say .5mm from the bed when it starts and ends up 2.5mm?

Diagnosing the head is lifting should be easy enough. Observe the Z axis motor as you start your print. If it turns a bit, there's your issue. Something may be telling it to lift a bit, or something is physically forcing it to lift. Disconnect the Z motor from the board if you can, and if it still lifts, it's being forced to lift.

Calling your bed level is sort of ambiguous in this situation. If the metric you are using to level the bed is inaccurate itself, then it will give you a false reading. Get a dial indicator and confirm the bed is actually level. Mount the indicator next to the print head, and run it by hand over the bed surface. If you are already using a dial indicator, then the leveling procedure has a flaw in it (I truly doubt a dial indicator would give identical results over multiple trials if it was broken). Look at your procedure and figure out what you could be doing to induce an erroneous reading. Maybe your hand is pushing down a bit in one place.