Note that the definition of i is that it is the number such that i=√-1. This means that i2=-1. Squaring both sides means i4=1. Multiplying both sides by i then implies i5=i.
So to figure out (-i)^5 first notice that
-i = -1*i
=> (-i)5 = (-1*i)5 = (-1)5 * (i)^5
Here you should notice that -1 to an odd exponent is always -1 and i5=i. So
(-1)^5 * (i^5) = -1*i = -i
So finally 2+(-i)^5 = 2+(-i) which is not a real number. The answer is false.