5'7 isn't freakish, it's distinctly normal for an adult so she should get normal adult clothes and stop the whining.
At 13, a 5'7" girl is probably going to be pretty skinny, as is the case here. Puberty involves growing in a lot more than just a vertical sense; she's probably got another 3-4 years before she fills out enough to wear adult clothes, and in the mean time, she's going to have to make a choice between fitting length and fitting width. Given how fitted most women's pants tend to be, fitting width is going to result in a much more comfortable garment than getting something longer that ends up being baggy and bunching in awkward places.
Also, average for adult women is 5'4", so that's definitely not "distinctly normal." She could easily shop men's clothes, certainly, but that's another beast entirely (if you thought she had to make compromises in proportion buying girls' clothes...), and telling a teenage girl to just buy men's clothes isn't exactly going to help her self-esteem.
This is just giving it more attention than it needs. Protocol is protocol. Her daughter is tall. We get that. But she shouldn't be picky either. She can't be hard to shop for and picky at the same time. She can't have her cake and eat it too. There needs to be a compromise somewhere. ---
"Ladies don't start fights, but they can finish them." -Marie, Aristocats