Think you'll find different councils have different rules and charging regimes.
In our complex of 20 units each resident has their own bin for general waste, and we share 7 recycling bins which are collected fortnightly. With general waste, our council offers either weekly collection at one rate, or fortnightly at half that rate. Bins are identified by a different lid colour.
You haven't stated whether the 5 bins are sufficient for your complex, or whether there is room for an additional 11 bins. Perhaps it was considered by your managing agent or committee that 5 bins was enough. If each unit owner is being billed for a bin the same as all your neighbours in separate houses, don't see why you can't insist that the council provide each unit with a bin. It worked for us when council tried to institute shared bins against our wishes, get onto your local alderman if you don't get anywhere with bureaucracy.