Is the Calculation of 4 Fringes Correct Instead of 5?

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SUMMARY

The calculation of fringes in a single-slit diffraction pattern is confirmed to be 4 instead of 5. The discussion clarifies that the single-slit minimum cannot occur at the 5th fringe, as this position must correspond to a bright fringe. Instead, the minimum lies between the 5th and 6th fringes, indicating that the second minimum is located between the 10th and 12th fringes, thus validating the conclusion of 4 fringes being correct.

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Miike012
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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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