I think this is a huge part of it. Even something as simple as free high-quality condoms or emergency contraception (morning-after) can make a huge difference when money is tight.

Even better would be free birth-control medication or IUD's, as these put the birth control in the hands of women, while condoms especially might not be used in the face of social pressure.

I like the assumption that the 5+ kids are all just due to irresponsible people popping children out and not, say, the results of generous people fostering family members who would be in even worse situations otherwise or a mother who is being raped by a partner.