The evidence would for the sponsor, i.e. the family member who was exercising treaty rights for 5 years. The Home Office guidance for PR applications says the following:
  • evidence of exercising treaty rights for EEA national sponsor, such as 5 consecutive P60s if employed. Otherwise, see the relevant guidance for self-employed and self-sufficient; and
  • proof of relationship between the applicant and the sponsor (one of either a marriage certificate, birth certificate, adoption certificate)
  • For the applicant, one piece of evidence for every qualifying 12 month period to confirm residence in the UK; and
  • one piece of evidence for every qualifying 12 month period to confirm ongoing residence in the UK if more than 2 years has elapsed since the end of the activities.
See: Evidence of residence - this is to prove the sponsor's residence for the purposes of exercising treaty rights and/or acquiring PR status.
Citizenship applicants will also need to provide evidence of their own residence during the last 3 or 5 years, as noted here: Evidence of residence

If the sponsor already has a PR card, the card itself would be proof of having exercised treaty rights for 5 years.

See also: Evidence for couples living together.

Children also need to have lived in the UK for 5 years to apply as dependents on their parent/carer.

Whoever has been exercising treaty rights for 5 years is the main applicant.

Once either parent has PR status, the child can be registered as British if born in the UK.

See How to register children as British.

Evidence for children
  • evidence of school attendance
  • nursery attendance for pre-school years
  • red book
  • doctor’s records
  • vaccination records
  • attendance to playgroups and other local groups.