Hi Lisa Dawn, welcome to CB!
From a coaches perspective I'd say at 5yrs old, the most important thing to consider is whether or not she is having fun.
I know a lot of people will say, fun/enjoyment really is the only factor at this age, however, I believe there are some things that you should watch out for with a particularly talented child:
Make sure her coaches get all the niggly things sorted like pointed toes, straight legs, stretched arms and fingers etc. This can be done in a fun way, and it doesn't have to make the gymnast feel that they are being nagged at.
It is also really important that the skills are taught correctly - try to familiarise yourself with what good form is - perhaps look at youtube, you will soon easily spot the difference between good and poor skills.
I also think it is important that the gym knows competition rules!
I say these things from having watched gymnasts with a good amount of talent be let down by their coaches lack of effort! There is a particular club in my region who bring gymnasts along to competitions. More often than not these gymnasts are unprepared, physically, for the level they are competing. However, every once in a while, they bring gymnasts who are more than capable of scoring well, but because the coaches haven't bothered to read the rules properly, the gymnast's scores have suffered - they often have barred skills in their routines, or the coach remains on the podium when the routine has begun etc. There are also many clubs who don't make any effort with choreography or really 'polishing' the gymnasts performance.
Ok, I'll get off my soap box now!
Anyway, to summarise - I do think the most important thing is whether your DD is having fun in the gym and that she gets along with her coaches and they bring out the best in her.
I would let her compete and see how she gets on. Also while you are at the competition, check out the other gyms, see how their gymnasts perform, see how other coaches behave towards their gymnasts - do they congratulate them for a good performance and console them for a poor one, or do they ignore the good and scold the poor? (I've seen a lot of the latter!)
There is no harm in looking and even visiting other gyms to see how they work but you don't need to cross that bridge until you come to it! You never know, you may already be at the best place for your DD.
Finally, be led by her - if she starts not to enjoy herself, perhaps think about a move. If she loves it, I'd leave her where she is, unless there is a reason YOU aren't happy (and it has to be a good reason!)
Sorry for that long post, and I hope it wasn't too much info, I just couldn't stop typing once I got started!
Marie