The firms are competing to create a design for the park, which will undergo a £6m revamp. The Bidders Day gave local people a chance to tell the hopeful firms what they want incorporated in the design.
Earlier this year, Burgess Park was awarded a £2m grant from London mayor Boris Johnson's Help a London Park scheme.
An extra £4m of match-funding was awarded by the Aylesbury New Deal for Communities towards the work on the Southwark Council-owned park.
The five shortlisted bidders are LDA Design, Patel Taylor, Gillespies, Building Design Partnership (BDP) and The Landscape Partnership.
Southwark Council executive member for regeneration councillor Paul Noblet said: "We want the bidders to come up with a masterplan that takes into account all the concerns and wishes of the public... so everyone benefits from a first-class revitalisation of the park."
Johnson added: "It is absolutely critical that Burgess Park is revamped to suit the people of Southwark and help make their future experiences of it far more pleasant."
The £6m will be spent on: creating different habitats; removing redundant roads and pathways and making those that remain more user-friendly; giving the park a striking identity with new artwork; and creating improved entrances and better-defined boundaries.