What does 1 Timothy 5:4 mean?
The first phrase, regarding children or grandchildren, is not about whether family members are believers, but whether a widow has living family who can help care for their needs. Immediate family is always the first recommended step for assistance to widows in the church. This is true whether the widowed woman's help comes from a child—either a son or daughter who is old enough to provide help—or a grandchild. Later verses will point out that Christian believers are particularly obligated to care for their families (1 Timothy 5:8)Again, the concept of "godliness" is mentioned in connection with serving others. Here the specific context is that of widows. The purpose of encouraging family to care for their elders is so that children and grandchildren can repay the investment made into their own young lives. According to this verse, "this is pleasing in the sight of God." This idea of "pleasing" is the same one Paul uses in 1 Timothy 2:3 regarding prayer for all people, including kings and governing authorities.
First Timothy 5:3–16 gives Paul's instructions regarding priority in the care of widows. Since church resources are finite, it is important to focus attention on those who are most needy. In this case, Paul refers to such women as ''true widows.'' Those who are younger or more capable should not be given an excuse for laziness or gossip. And, family members have the first and foremost responsibility for caring for each other. The guidelines given here focus attention on the most vulnerable women and avoid enabling immodest behaviors.
First Timothy chapter 5 focuses on Timothy's supervision of those within the church. This includes a respectful attitude towards both men and women, young and old. A large portion of the chapter deals with how to care for widows. The theme of Paul's instruction is prioritizing those who are truly in need, and not enabling those who are merely lazy. Timothy is also instructed on how to screen out baseless accusations against an elder, and how to properly discipline them if they are found in sin. With that in mind, Timothy is also warned not to be reckless in who he appoints as an elder.