I'm not going to offer any advice as I think you know what is best for your child, but I will just add my experience as another parent who can sympathise with your plight as I have been there, done that myself, with my own child.
My older child missed the cut off for school by 3 days (

) and so he was 6 and 1 month when he started grade 1 (birthday fell during the school holidays). No problems. He is in grade 5 this year. Had his birthday been 4 days earlier I would have had no hesitation in sending him into grade 1 at the age of 5. I had the opposite situation with my younger son.
My younger child made the cut off by 1 month so we had to make a decision. He was/is very small for his age (despite being a big baby at birth). He was a somewhat immature during his preschool year (US kindergarten I think) but he was very bright and I knew if he repeated pre-school he'd be bored and drive everyone nuts. We ummed and awed and spoke to his pre-school teacher. At the mid year point she said he was borderline for repeating pre-school, but by the end of the year she said he was fine for grade 1. We sent him to grade 1. It was the best thing we did. He thrived - he was constantly in the top 5 for work results and received an award at the end of the year for most improved. For the first few months I have to admit I wondered whether he was mature enough, but almost literally overnight at the end of term 1 he "clicked". He's never been keen on change but I think the routine of school really appealed to him. At the end of year parent/teacher interview his teacher said he one of the most mature boys in the class, which I have to admit, I never thought I'd hear, but she's the one who was there day in and day out with all the kids so I suppose she's in a better position to judge than I am/was.
I spent a
lot of time helping in his classroom in grade 1 and from that experience can say that age had nothing to do with whether the children (in that class at least) were mature/acting age appropriately. Some of the oldest kids in the class still didn't seem to "get it" by the end of the year. This year he is in grade 2 and some of the (older) kids in the class really should still be in grade 1 maturity wise, and a couple of the first graders (I help in both classes) could easily fit into grade 2, and it's only been a month since school started.
Some of the biggest children (size wise) are also some of the oldest, and I don't know whether it's just these children, or whether it's universal, but they don't seem to know how to act appropriately around the smaller/younger children (very rough) - perhaps that is a sign of
them being immature? I'm not an expert so I don't know, just merely an observation. My son is still the smallest in his grade, and most of the 1st graders are bigger than him too, but that makes him easy to identify and he's never let it bother him.
I know parents who have held their children back and regretted it, and others who have been pleased with their decision. I also know children who have started grade 1 and then returned to pre-school a short while later (in our system it is possible to do it this but it is not possible to start p/school again and then transfer up to grade 1 during the year). And then there are others like me who decided to take the chance and were fortunate that it worked out.
Good luck, as I know it can be a tough decision.