1 Timothy 1-5: Here is a Trustworthy Saying

In Paul's first letter to Timothy, the young man he considers his son in the faith, he is trying to give Timothy a solid background that will enable him to be more effective.  He in instructing him so that he will have the tools to command certain men not to teach false doctrines any longer nor to devote themselves to myths and endless genealogies. These promote controversies rather than God’s work—which is by faith. The goal of this command is love, which comes from a pure heart and a good conscience and a sincere faith. Some have wandered away from these and turned to meaningless talk. They want to be teachers of the law, but they do not know what they are talking about or what they so confidently affirm. - 1 Tim. 1:3-7 NIV

Rather than teaching with no background, Paul wants Timothy to fight the good fight and hold on to the faith. Guard what has been entrusted to your care, he tells him.  Don't take part in godless chatter or entertain popular ideas which are falsely called knowledge. Instead concentrate on those things which are known to be true.  Paul gives Timothy several 'trustworthy sayings' that he can count on.

Here is a trustworthy saying: If anyone sets his heart on being an overseer, he desires a noble task. Now the overseer must be above reproach, the husband of but one wife, temperate, self-controlled, respectable, hospitable, able to teach, not given to drunkenness, not violent but gentle, not quarrelsome, not a lover of money. - 1 Tim. 3:1-3 NIV

This is a trustworthy saying that deserves full acceptance (and for this we labor and strive), that we have put our hope in the living God, who is the Savior of all men, and especially of those who believe. - 1 Tim. 4:9-10

But perhaps the most 'trustworthy saying' is the one that is the most important for all who profess Jesus as Lord.  Here is a trustworthy saying that deserves full acceptance: Christ Jesus came into the world to save sinners—of whom I am the worst. But for that very reason I was shown mercy so that in me, the worst of sinners, Christ Jesus might display his unlimited patience as an example for those who would believe on him and receive eternal life. Now to the King eternal, immortal, invisible, the only God, be honor and glory for ever and ever. Amen. - 1 Tim. 15-17 NIV

Paul knew what it was to receive mercy from the eternal, immortal, invisible, only God, through Jesus Christ.  He knew it was trustworthy because he considered himself to be the chief of sinners and knew the change that had been wrought in his life.  Paul wanted Timothy to understand and convey that gospel as well...that Christ Jesus came into the world to save sinners...of whom I am the worst.