Commenting on Psa 110:5, Mitchell Dahood suggests that the Masoretes were incorrect in their vocalisation, and that it should read, not Adonai but adoni:
my lord. Revocalizing MT adonay as adoni, the term designating the human king in vs. 1. Structurally, adoni corresponds to ‘attah, “you,” so that the following parallel elements stand forth in a chiastic pattern: You // my lord; priest of the Eternal // His legitimate king; according to his pact // according to your right hand. (Mitchell Dahood, Psalms 101-150 [AB 17A; Garden City, N.Y.: Doubleday, 1970], 118)
As with the vocalisation of ADNY in Ezra 10:3, this is perhaps another instance where the Masoretes erred vis-à-vis the vowel pointing of the Hebrew text.
For some more discussion and debate as to the importance of this, see the to-and-fro between Stephen Cook and Anthony Buzzard, two Socinians (Christadelphian and Church of God Abrahamic Faith, respectively) in the comments section here.