From this wording it seems we want the probability that

*exactly* 10 consumers recognize the brand out of 15 randomly selected, rather that

*at most* 10.

If we assume an infinitely large population, then when picking out random consumers without replacement, the event that one consumer recognizes "ABC" is independent from the event that another consumer recognizes "ABC," always with probability 0.95.

So the probability we're after is

$\displaystyle P(X = 10) = \binom{15}{10}(1-0.95)^{10}(0.95)^5$.

See

here for more info.