It looks like by this Muster Roll that she was still the Flag of DESRON 4 in September.
In 1939, Selfridge was flag for DESDIV 4. Mugford was in her DESDIV. With the newer Benson variants coming on line, could she have somehow ended up in DESDIV 5? Does anyone have the DD ORG charts for 1941?

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These photographs show USS Mugford DD-389 and USS Selfridge DD-357 moored at the PH Naval Yard on September 9, 1941. One thing that caught my eye is the number "5" painted on the side of Selfridge's #3 turret.
Anybody have any idea why there is a "5" painted on that turret?