Do I need to purchase a ticket for my 5yr old to see a Bears game? Or is it based of height of a child vs age?

Under 32" no ticket over then yes

Child Ticket Policy…Children under 32” tall are permitted entry inside Soldier Field without a ticket provided they obtain a complimentary lap pass prior to entry. Ticketed patrons will need to obtain a lap pass at the Gate 10 Ticket Office at Soldier Field on gameday. The child receiving the lap pass must be present when the pass is issued. There is a limit of one lap pass per game ticket. The child must sit on a ticketed patron’s lap for the game and may not occupy a seat.