The bad thing: Your Phd is yet nothing, it is a plan what you say. If you apply for a visa extension because you are a running Phd course, yes that is something.
The students lie because they fear the rejection of their visa. Particularly the USA is infamous in this sense. The German authorities know it very well, more clearly the responsible officers know it, but they follow the directives what they got from the higher levels.
The real effect to the probability of the Visa rejection is probably small, if the student say some different than "yes". Obviously if he states to plan any illegal, that had a very bad effect, but it is unlikely that well-educated people would do that.
However, saying a "yes", on that paper, is practically nothing. Well, you said 5 years before that you plan to go home, however you got a wonderful job offer as a young Master of ..., so you changed your original plans, there is nothing bad in it (and particularly nothing illegal, at least if your employer sponsors your visa).
Note, 5 year is already close to the 8 years where you can apply for citizenship. I do not know the exact rules, but if you are here since 5 years as a student, you are probably close to get at least some "permanent resident" or similar status (meaning that you won't be sent back, except hard cases like being convinced or similar).
In practice, today millions of people live in Germany, with zero German or English skill, with a low-level elementary education, and with zero intention to integrate into the society. The government tolerates it on political reasons.
These directives actually prefer well-educated workforce.
Getting a job after the Masters, yes that will be hard.
Getting the VISA, that is not.
But honestly, also I would say a simple "yes" - simply because it has no relevance for the future.