That’s the way some people are looking at it: 5x-5x=5 cannot have a solution (that is, cannot be true), because if we assume that it is true, this leads to a contradiction (0 = 5).
But that’s not the way I’ve been looking at it (in my earlier posts #11 and #22). I’m just saying that 5x-5x=5 is equivalent to 0=5, and since the latter has no solution, the former also has no solution. I don’t think there’s any need to invoke the LEM—is there?