Upvote:6
Everyone applies on a different application. Everyone needs to fill their own form (or have someone fill it for them), deposit their own fee, take their own appointment and everyone needs to pay for the appointment.
However the appointments for a family can be booked so they they attend together and the supporting documents can be linked together and will be sent to UKVI in one package by the VFS staff. For example: You do not need to print 5 copies of your mother's bank statements for each one of you. Just 1 copy is fine.
Of course your mother can pay for all of you on her card but she needs to pay for 5 applications and 5 appointments.