There's several ways this could be done.
All new coil stock could be installed that would be wider, not a cheap job because there's going to be a lot of waisted material. With A normal fashia you can get 3, pieces out of every section cut off the roll. Since it's wider you can only get 2, the rest is trashed.
A much simpler way would be to simply add vinyl baseboard moulding upside down. It would cover that gap, look good, never need painting, simple to install, it will extend the shingles out more so there's less chance of black stain on the fashias from dirt running off the roof.
Make sure they add drip cap as there install the new roof.
It would act like shingle moulding but would be wide enough to cover the gap. You may want to rip it so it's not as wide if all you can find is 5-1/4" base.