“O almighty Lord.” The context supports that this is to be translated as a vocative, “O Adonai,” and is addressed to Yahweh (cp. NET and Rotherham, who both translate it as a vocative). The psalmist, David, is speaking (David is the psalmist, cp. Matt. 22:43-45). This is the third Hebrew word in this Psalm that is translated “Lord” in most English versions. “Yahweh” and “Adoni” are in Ps. 110:1, and here in verse 5 is “Adonai,” which is from the same root as Adoni, but is a different word with a different meaning.
“at your right hand.” This is addressed to Yahweh; “your right hand” is Yahweh’s right hand, as was already stated in Psalm 110:1, that the Lord (Messiah) would sit at Yahweh’s right hand.
The Hebrew text can also be “by your right hand,” meaning that it is by Yahweh’s power the Messiah will shatter his enemies. In that sense, the Messiah would be understood to be the “right hand” of God (Exod. 15:6). However, it is perhaps better to see the Hebrew as saying “at” your right hand, based on verse 1 of the Psalm. The Septuagint agrees with this meaning of the verse and is “Lord, out from (ek) your right hand he crushes kings in the day of his anger.” Thus in the Greek text also there is a clear distinction between the “Lord” and “he” who crushes kings.
“is he who will shatter kings in the day of his wrath.” In Psalm 110:5 there is a shift to the third person, “he” and “his.” Psalm 110:2-4 used the second person “your” referring to the one at Yahweh’s right hand (the Lord, the Messiah). Now the third person, “he” and “his,” refers to the Messiah. The verse starts with a direct address to Yahweh.