Is the Calculation of 4 Fringes Correct Instead of 5?

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The discussion centers on the calculation of fringes in a single-slit diffraction scenario, with the original question suggesting five fringes. The responder argues that the correct number of fringes is four, stating that the single-slit minimum cannot occur at the fifth fringe since it must be bright. Instead, the minimum should be located between the fifth and sixth fringes, leading to the conclusion that the second minimum falls between the tenth and twelfth fringes. This analysis results in possible answers of five or six fringes. The conversation seeks confirmation of this calculation.
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Question are in paint doc. My answer is in red... I believe the answer is 4 and not 5. Please someone let me know if I'm correct.
 

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The single-slit minimum cannot be at the 5th fringe on one side, as this has to be bright. The minimum has to be between 5 and 6, so the second minimum is somewhere between 10 and 12 (not inclusive). This gives 5 or 6 as possible answers.
 
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