I know you don't want advice, but you posted in a gymnastics forum so you're going to get it.
Your daughter is doing very well, but she does not have all of her level 5 skills and you are considering moving her to Level 6, why?
Many gyms do not let a child compete a level until they have all the skills. Some gyms do, but many don't. If you move to the new gym and she goes on the level 6 team, when do you think she will learn her level 5 skills?
My DD was in a gym that only cared about "IT" kids that would be going to elite in the future. Kids that struggled were just pushed along and not coached. My DD REALLY needed to repeat level 5 (she actually needed to repeat level 4, but the gym would have none of that). Anyway, the coaches for level 5 could be very cruel so I wasn't going to have her repeat it. So she went to level 6 and started having more and more fear in the gym and anxiety issues outside of gym. Anxiety disorders do not run in my family or my husband's family.
So... I got her out of there and she is at another gym nearby and is repeating level 5. She is doing really well and the skills that she just couldn't seem to get (such as FHS vault and FHS on floor and ROBHSBHS on floor, etc.) are all coming together at new gym.
Now when I say she couldn't get them this is what I mean; FHS vault (AWFUL - BALKING), FHS on floor (bent knees - looked identical to your DD's), ROBHSBHS (bent legs & wide legs on second BHS). DD wanted to quit when she got to new gym because the conditioning was so hard and it was so much work. She really wasn't being coached at old gym, so the new work ethic at the new gym was a real shock to her system.
These are the skills your DD does not have just for level 5:
Beam
Handstand - Scale - Dismount, Leaps are so-so.
Vault - coming along.
Bars - Saw no bars, read ppl reporting that DD does not have kip which means she's also missing lots of connections
Floor - Back Ext. Roll, FHS (bent legs means she doesn't "have" it), Leaps are weak, dance is weak.
I also saw lots of wobbles on floor and beam. Didn't see that when she competed level 3. Again, why rush to 6 when she doesn't have 5 down pat? She is only 7, she has PLENTY of time. Level 6 skills are not only harder, but they build on 5 skills. Not only will this make learning 6 skills harder, but it will make it more DANGEROUS. Tucks, fly aways, mean more risk for injury. Especially if the child is not ready.
I would have her only go to 6 next year if she shows she is ready. Better yet, have new gym evaluate her rather than just put her on their level 6 team, cause she competed 5 earlier in the year. FYI, if they are just sticking her on their L6 team, sight unseen; you should RUN not walk away. She should be evaluated and placed where her skills, physical abilities place her.
It was only 6 months ago that you video'd your DD at level 6. She had one level 5 meet where she didn't even score a 31 (which is a very low score, BTW). And now you're talking about her moving to level 6 next year anyway. She needs more time and experience at level 5 before taking on level 6, IMHO. Gymnastics is a marathon, not a sprint. Mariposa talked about burnout. What she means is that kids that go too fast in this sport often burnout. They don't have enough time to adjust to the exponentially increasing amount of difficulty and pressure.
You will do what you think is best for your daughter. Just beware of thinking that the gym has her best interest on their agenda. This may not be and often is not the case. Our old gym certainly did not have my DD's best interest on their agenda and they caused emotional damage that we are having to repair. It is not fun and I wouldn't want to see anyone else go through it.
! I'm just wondering why the push on in levels with a family move going on at the same time??? Our family moved when DD was in 1st grade & it was a big adjustment for her. In fact, DD even requested to drop back her gym hours back then, instead of going right onto a team. Moving is very stressful for kids. I would think letting J have a sense of being "settled" with her skills(owning them & polishing them) may bring her some comfort & confidence during this major life change for her(as she gets used to her new home, school, friends, gym, coaches, etc). Let her own what she has for a while, instead of pushing on for more. 
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, which includes a smooth transition to her new home & a life long love of the sport she enjoys so much now.
