Also, in the Douay Rheims, there's a small footnote there which explains what the Church teaches regarding the entire phrase. Notice there's a colon there.
(vs 5)For there is one God, and one mediator of God and men, the man Christ Jesus: (vs 6)Who gave himself a redemption for all, a testimony in due times.
(vs 5)One mediator: Christ is the one and only mediator of redemption, who gave himself, as the apostle writes in the following verse.
Also, regarding verse 6:
(vs 6) a redemption for all: He is also the only mediator, who stands in need of no other to recommend his petitions to the Father. But this is not against our seeking the prayers and intercession, as well of the faithful upon earth, as of the saints and angels in heaven, for obtaining mercy, grace, and salvation, through Jesus Christ. As St. Paul himself often desired the help of the prayers of the faithful, without any injury to the mediatorship of Jesus Christ.