The year of flat prices isn't a shocker, as valuation levels were rather above average a year ago. Things look a little better now. If nothing else, Berkshire was buying shares at $495 in July, so purchases at $503 today probably aren't going to make you go broke.

What is your expectation, for both BVPS growth and for price increase.

I'm willing to give it a stab.
Relatively normal rates, which might count as a bit optimistic these days...all bets are off if something snaps in the world economy.

Book growth 8.2%/year rate nominal (2%/quarter compounding)
Ending multiple 1.43 times book
So, maybe Q3 2027 book around $385 which will be known next October, price around $550, upside from today's $503.50 of nominal 9.2%?

Unless something breaks.
There might be a dip in book per share in a bear market (remember those?), but I'd ignore those dips, assuming it's always transient and not really reflecting a drop in value. For good returns in the next five years, what Berkshire needs more than anything else is a deep bear market.

Jim