Sum of 1s

Can you find the last 5 digits of this sum?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative


What are the last 5 digits of the sum $1+11+111+1111+\ldots+\underbrace{111...111}_{\text{2016 digits}}$?

This problem is adapted from the World Mathematics Championships