Verses 5 through 8a speak of a male goat.
The male goat signifies Greece with Alexander the Great (vv. 5a, 21a; 11:3).
This male goat came from the west (8:5b). This signifies that it came from Europe, west of the Mediterranean Sea.
The goat came over the face of the whole earth without touching the ground (v. 5c). This signifies its swift movement over the earth.
The goat had a conspicuous horn between its eyes (v. 5d; 11:3). This signifies Alexander the Great as an extraordinary horn distinguished by his two sharp eyes. He was very intelligent.
The goat came up to the ram in his mighty wrath, struck the ram, broke his two horns, threw him to the ground, and trampled him. The ram had no strength to withstand him, and there was none to deliver the ram from his power (8:6-7). This indicates that Alexander the Great conquered Medo-Persia and destroyed it.
The male goat became very great (v. 8a). This indicates that Alexander the Great became arrogant in himself.
Once the male goat became strong, the great horn was broken (v. 8a). This signifies that once Alexander the Great, the great horn of Greece, became strong in power, he died.