Is 5-6 the typical player count or is it usually 4 or less? A lot of games max out at 4 or play too slow with more. There are plenty of great games for 5-6 or more but its an important consideration.
For 5-6 my picks would be Challengers, 6 nimmt!, various roll & writes (Welcome To, Super Mega Lucky Box etc), 7 Wonders, It's a Wonderful World (might need expansion for 6), Sushi Go Party, Tiny Towns.
Games with fast turns or simultaneous play.