We had a nanny, but again the pressure of "he has to be socialized" by everyone (from grandmas, to pediatrician, to other moms) is why we explored a day school.
Honestly, we got a lot of that kind of pressure, too. I drove myself nearly round the bend trying to find somewhere that WOULD take my then-3yo for preschool, in light of her food allergy situation.
We got put on waiting lists, our applications got lost, and we otherwise walked away from preschools thinking "OY-- just-- no."
We never found one, and while my mother-in-law was pretty convinced that this meant enmeshment at the very least, and probably sociopathy down the road, I'm pleased to report that my daughter (who was similarly appalled at what was considered "age appropriate" conduct on the part of agemates) seems to be empathetic, kind, and generous at 14. Moreso than some of her peers who were "properly" socialized.
Remember, your goal is to produce a functional adult at some point down the line, not to be produce a 5yo who can fit in with all of the other five year olds at kindergarten.
With HG+ children, all too often that particular option is just never on the menu to begin with, so energy spent trying to make it so is really just WASTED effort.
I'm also going to gently suggest that given your child's age, you should look at the "homework" thing and ask if there is a BETTER way to be spending that time-- these are years that you won't get back, and they are wondrous. He has time for homework and externally-directed academics later. Developmentally, there are windows for play and exploration that will not be open for much longer, however...
my only concern would be that the TIME spent doing homework sent home by the preschool might be displacing family time that could be spent on something else-- something that might still be academic in nature, but would be what HE chooses, not what someone else offers. Does that make sense?