Couldn't agree more with the above. Teaching him properly, now, will save him a world of misery later. It's so much easier to learn correctly the first time, than wait to fail with standard teaching and have to unlearn/ relearn whilst ridden with anxiety and falling ever-further behind. Furthermore, if his teacher is already flagging the problem when he's only five, that suggests dyslexia may be having quite significant impact already.
I get where you are coming from with having him properly recognized later, though. Gifted dyslexics can compensate so well they look like they don't need any special consideration, but they have to work so incredibly much harder to keep up, it's not a level playing field. I'm not sure what kind of testers you've called, but maybe keep calling? In particular, are you able to access a psych who specializes in 2E? As PB notes, the underlying phonological deficits are quite detectable, even at 5, to someone who knows what they're doing. If you can get the dyslexia documented now, and also start remediating now, that's the best of both worlds.