When you create a multi-signature address using pay-to-script-hash (p2sh), you create an address by hashing a redeemscript (hence the name). This redeemscript specifies the requirements to spend any funds sent to the resulting address. To lock funds to a quorum of 3-of-5, you will need to include the five public keys of the involved parties in the redeemscript. Therefore, neither addresses nor private keys are needed to generate a multi-signature address, but all five public keys must be known to the party that creates the address. As the redeemscript (and therefore the public keys) is revealed at the time of spending funds sent to the address in the transaction's input script, there is no expectation of keeping the public keys private in the long run.
To maintain privacy, the five participants should each generate a new key pair for this multi-signature address instead of reusing an existing public key. They could however use their existing public keys to authenticate the new public keys by signing a message stating their ownership with their old public key.