Such a strange requirement 'brown strap' :D You can buy anything and put it on a brown strap you know? :)
For under $5k, in the not too dressy/not too casual field, you have NOMOS and Tudor offering nice stuff.
But honestly, for that price, I'd go vintage.
I'm currently leaning towards the JLC. I'll just take a years worth of French classes or something. And yes I know you can put a brown strap on anything but in my mind I picture a brown leather watch and a black leather watch as two fairly different looking things if that makes any sense.
Youre up to the task. I believe in you. No one on youtube can pronounce it either if thats any consolation. What about cartier tank ? Vintage or new seems to be right around 5k , maybe a little more for a new gold one , but youre worth it.
I thought about nomos but idk, just doesnt scream lyle to me . There is always a vintage datejust or tudor or something. Obviously like the other poster said you can put a brown strap on anything , but you already know that.
As for Nomos and Tudor, I'm not a huge fan of either although admittedly I haven't spent much time looking at Tudor watches before.