I thought first gear didn't have synchros. Am I wrong?

 

1st gear has synchros. It is reverse that you are thinking of that doesn't have synchros.

 

I know that in my 5th gen prelude and my 4th gen before 5th gear always grinded if I was going a slow speeds. But whenever I shift in vtec there would be no grind, If I'm driving on the highway at respectable speeds and shifting from 4th to 5 I have to rev match with the clutch to 3500 to get a smooth 5th gear engagement. I don't have any problems shifting into 1st when coming to a stop but then again usually downshift through all gears before coming to a stop and only go into 1st gear from 10mph or below. If you're not having any trouble shifting into 1st from a complete stop then I wouldn't worry about it, if you are a synchro may need replacement and without warranty better to just replace with a used tranny. But the infamous 5th gear grind is prevalent from Honda, I believe even the RSX-S has it.