Test for a certain disease

Testing for a disease. has 0.02 probability of giving a false-positive reading and probability of 0.03 of giving a false-negative result. (a false-positive means testing postive for the disease when it's a healthy person).

5 people are test, two of whom have the disease and three who don't. X=number of postive readings.

I am going to assume this is a binomial distribution and there are only 2 outcomes (postive or negative for disease). Right?

What im having trouble with is the probability that at most 2 of the 5 tests results are positive.. I am confused where to start this (Nerd)