If there are only 16 tickets sold, and you bought 5, then you have a 31.25% chance of winning. Each ticket has a 6.25% chance of winning. So yes, there is only a 1 in 16 chance any given ticket is pulled, but an overall chance of 31% that it's one of yours.
From my understanding this draw has 80 tickets sold which results in a 1.25% chance per ticket bought. Glad there's no freeloaders in this one with essays.