The contract Turris signed when adjusted for cap inflation would come in at just about 4.75M per for 5 seasons. Alex Tuch signed for the same AAV, but it was for 7 seasons. I'm not sure how many UFA years Turris' deal bought up. That is another element that changes things. Some RFAs have burned through more years than others and expect a higher salary on a longer term deal because it buys up more UFA years.
Turris was a bit more productive (measured by P/PG) in his lone season with the Senators prior to signing than White and probably had a higher perceived ceiling.
Using just one comparable doesn't always work, but even without the Turris comparable, my gut tells me 4.75 would be high for a 5 year term. Judging by some things Dorion has said when publicly evaluating our group of prospects, I don't think they perceive White to have much more of an offensive upside than what he showed this season. He seems like a guy penciled in to be our middle 6 center going forward.
We haven't signed a real long term contract since Ryan. I'd be shocked if White is the player that we break that with. I would guess that maybe it would be a 3 year contract. Sens probably want 2, but it wouldn't be smart for White to agree to 2 because then he risks having to negotiate his next extension after not being able to showcase himself if there is a lockout.