What genuine-looking reason should I give to HR in an interview for not having worked in the last 6 months if I have 5 years job experience?

When I have taken time off, I have tried to accomplish things even if it was a much-needed break, a house project, spending time with my family, travel etc.

Taking 6 months off after working for 5 years is not a bad thing. I have made a habit of taking time off between stages of life (school, work, having babies etc). It is good for the soul and nothing to apologize for. I have never felt that it has hurt my career progression, nor have I felt penalized or judged in an interview as a result.

When I have taken time off, I have tried to accomplish things even if it was a much-needed break, a house project, spending time with my family, travel etc.

So, I would be unapologetic, explain why you took the time off and be ready to discuss what you accomplished.