Yes namely 2 ,3, 4 and 5 but if you mean two solutions than the answer is also yes because -2, -3, -4, -5 are also solutions.

However there may be even more solutions because Z27 is not a field. If We are working in a field then the polynomial x^2-4 can have at most two roots but in Z_27 it can have more.

EG 1 has 4 square roots in Z8 but only two in Zp for prime p.