I fear the 5 sec hang will be a failure, though I could be wrong in that the pushups may save her. If she can do 49 pushups, I guarantee she can hang for 30 seconds. The flexed arm hang is, IMHO, as much mental as physical -- and I say that as someone who did it.
Sounds like she has a hang bar. If she does, have her use a step stool and start from the hang position. Do a few reps in the morning and a few in the evening (hold as long as she can and SLOWLY allow her chin fall below the bar). I'm 99% sure that, within a month, she will be hanging like a fool and then can work on pull-ups.
If she passes the CFA with the above scores then not sure she needs to retake b/c all of her other elements were good to excellent (USNA really doesn't care about the BBall throw). And if she passes, USNA is in effect saying that it's focused on pushups over the pullups/hang. Nonetheless, she should continue to work on this during the year b/c there will be events during PS where upper body strength is needed.
Also, I don't think her size has much to do with it. I know a young woman who's 3" shorter and 1o lbs lighter who can do 9 pull-ups. Not saying that's the norm or expected, just that USNA is unlikely to consider height/weight as a mitigator since your DD is pretty normal in that regard.