11 Now the Messiah has appeared, high priest of the good things that have come. In the greater and more perfect tabernacle not made with hands (that is, not of this creation), 12 He entered the holy of holies once for all, not by the blood of goats and calves, but by His own blood, having obtained eternal redemption. 13 For if the blood of goats and bulls and the ashes of a heifer sprinkling those who are defiled, sanctify for the purification of the flesh, 14 how much more will the blood of the Messiah, who through the eternal Spirit offered Himself without blemish to God, cleanse our consciences from dead works to serve the living God? 15 Therefore He is the mediator of a new covenant, so that those who are called might receive the promise of the eternal inheritance, because a death has taken place for redemption from the transgressions committed under the first covenant. 16 Where a will exists, the death of the testator must be established. 17 For a will is valid only when people die, since it is never in force while the testator is living. 18 That is why even the first covenant was inaugurated with blood. 19 For when every commandment had been proclaimed by Moses to all the people according to the law, he took the blood of calves and goats, along with water, scarlet wool, and hyssop, and sprinkled the scroll itself and all the people, 20 saying, This is the blood of the covenant that God has commanded for you. 21 In the same way, he sprinkled the tabernacle and all the vessels of worship with blood. 22 According to the law almost everything is purified with blood, and without the shedding of blood there is no forgiveness.
Heb 8:6 But now hath he obtained a more excellent ministry, by how much also he is the mediator of a better covenant, which was established upon better promises.
Heb 9:15 And for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance.
Heb 12:24 And to Jesus the mediator of the new covenant, and to the blood of sprinkling, that speaketh better things than that of Abel.
1 Timothy 2: 1 - 15 - Study This Chapter
1 I exhort therefore, that, first of all, supplications, prayers, intercessions, and giving of thanks, be made for all men; 2 For kings, and for all that are in authority; F2 that we may lead a quiet and peaceable life in all godliness and honesty. 3 For this is good and acceptable in the sight of God our Saviour; 4 Who will have all men to be saved, and to come unto the knowledge of the truth. 5 For there is one God, and one mediator between God and men, the man Christ Jesus; 6 Who gave himself a ransom for all, to be testified in due time.
From Strong’s a mediator is:
- one who intervenes between two, either in order to make or restore peace and friendship, or form a compact, or for ratifying a covenant
- a medium of communication, arbitrator
In each of the above passages including your proof text from I Tim 2:5 Strong’s first definition of “one who intervenes between two, either in order to make or restore peace and friendship, or form a compact, or for ratifying a covenant” is the clear meaning. In fact at the beginning of the I Tim 2 passage we are told to perform “supplications, prayers, intercessions, and giving of thanks, be made for all men” thus anyone who is praying is not in conflict with Jesus as the “one mediator”.