I need to show my family what is a reasonable pay for caregivers, any advice?

Are you talking about one person doing 24/7 care or shifts of caregivers? I'm not sure it really matters, but perhaps the person proposing this absurdly low rate is thinking that the caregiver is sleeping at night and thus is not really "on duty". Except that we know that they are. Are you in the US?

$5/hour is an insult.

What are the hours and duties of the caregivers? What are the impairments of the person being cared for?

Pay would depend on exactly what is involved, but $5 is not acceptable for ANY level of care.

I'll answer it here, if you don't mind. $5 an hour isn't even minimum wage. Getting crap people? I'm surprised you're getting any people at all.