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I think this would depend on the specific situation. If it is possible for a respondent's rating to decrease due to the intervention, then no, respondents who had a pre-intervention rating of 5 should not be removed.
If, somehow, it is only possible for ratings to improve with the intervention, then you might want to exclude those who indicate from the outset that the intervention cannot help them.
In this latter case, it becomes a matter of selecting a sample that represents the target population. For example, if you were testing the efficacy of a cancer treatment, you wouldn't include people who didn't have cancer, as they wouldn't be getting the treatment anyway once it was tested and available. In the case of this 'intervention', the question for you to consider is whether people who already rate themselves a "5", would even be seeking or receiving this intervention.
Either way, you would want to be open and honest about your decisions when explaining your methodology. As long as those who are reviewing your results know exactly what was done and how the study was performed, there will be little room for any accusations of data manipulation, or other shady practices. The worst that could happen would be that your methodology is criticized by those who disagree with whatever you have done. But that would be much better than having your credibility impugned by accusations of data manipulation.
I hope this helps.