The early Christian church, like the modern Christian church, has both internal and external missions. It is important to not get hung up on the regulations spelled out here in chapter 5 but to focus on the principles outlined. In most of the ancient world women could not hold office, vote or even own property. A woman who had no children and had lost her husband would be totally destitute. The most vulnerable people in the first century were widows, orphans and sojourners (travelers and new comers to a community). The widow because she had no husband to protect her; the orphan because there was no father to protect him/her; the sojourner because there was no family to defend them. The fair treatment of these widowed women was a critical ministry issue in the first century. Notice that the institution of the office of deacon (see Acts 6) was over the issue of the food distribution to the widows in Jerusalem. The church must care for its own -- in 1 Timothy 5 we have this extensive conversation about defining which widows should be cared for by the church. Those widows that have families should be cared for by their families. Those widows who do not have families are cared for under the umbrella of the church. The early Christians did not stop there but were always extending their caring outside the walls. One of the great accusations from extra biblical literature of the first century is a complaint by a Roman official that the Christians not only took care of their own in need but the rest of the village as well (he seemed to think it made the Romans look bad). For the modern world, we have to ask: "who are the completely destitute and powerless in our society, in our churches, in our communities?" How then should the church respond?
The rest of chapter 5 is practical advice for community living -- treat elders with respect, don't ordain hastily, keep yourself pure. There is even a bit of practical first century medical advice (v 23).