Some very useful advice here. If I understand correctly, when arriving at T5 I'll have a choice to make (Door #1 or Door #2 as it were.) Door 1 will take me into the public areas of the terminal, and thus avoid immigration, customs, etc. Door 2 will route me out of the terminal and airside and through customs into England proper. This, if i get it correctly, is why I wouldn't be able to drop my bags at the Galleries lounge (it being airside.) But since my bags will be checked through to LAX, all I'd have with me are my carryon items.
I have to admit, however, that now I am torn about doing this little side trip (I have a choice of layover times and the 7 hour window would be by choice - I could also have a 2 or 4 hour layover.) While I've been to England maybe 20 times over the years, and traveled reasonably widely (most recently hiked the Lake District for about 10 days,) Windsor, Eaton and environs has never made it onto my radar. What makes me hesitate is the proximity to 2 of the 4 3* restaurants in the country. I've previously eaten at both the Dorchester and Gordon Ramsey (one of the top 5 meals of my life, btw) and now think I should reserve Windsor for a couple of day side trifp built around 2 really, really good meals.
Again, thanks for everyone’s help. I'm going to have to decide (and buy my tix) in the next couple of days and I have a lot to chew over