Flying in to ORD in CW then on to MSY in AA economy and am something of a newbie when it comes to transiting in the US.

My flight to ORD arrives at T5; onward flight to MSY has no terminal information in itinerary, but presumably T3.

What's the best way to get from T5 to T3 and how long should I allow?

And what's my best lounge option for a 3hr layover?

I see I'm entitled (thanks to GC) to use the BA First lounge in T5, but I note there are also several AA lounges at T3. My natural inclination is to get as far forward in my journey as possible, i.e. if onward flight departing from T3, use the lounge there. If so, which T3 lounge to choose?