This is a binomial distribution, since there are exactly two alternatives with known probabilities.
p = .60 (60%), q = 1 - p = .40.
The probability that exactly 4 out of 5 selected adults is the number of ways of selecting 4 out of 5 adults, which can be written 5C4 (which can be read as "5 choose 4"), multiplied by the probability the probability that each of these 4 adults believes in reincarnation p^4 = .60^4, multiplied by the probability that the remaining 1 adult does not believe in reincarnation (1-p)^1 = .40^1.
So the complete answer can be calculated as 5C4 * .60^4 * .40^1
Numerically, 5C4 = 5, .60^4 = .1296, .40^1 = .40
So the product of these is .2592
The general formula for the probability of the result of n independent trials resulting in exactly k "successes" when the probability of success in any single trial is p, is given by
nCk p^k (1-p)^(n-k)
As an aside, the above answer can be checked on wolframalpha.com by entering
(5 choose 4) * (.6)^4 * (.4)^1