No, they agreed on 5 years because the alternative was to pay Matthews the McDavid contract for 8 years. To say it was "to lower the cap hit" is inaccurate and revisionist history, it was because he wanted his comparable to be McDavid, instead of settling into a 8 year contract somewhere between McDavid's and Eichel's, which is what was expected his contract would end up at.
Matthews "settled" on 5 years to get him to UFA as fast as possible, in order to cash out for as much as possible, and your boy wonder handed him the keys (along with a NMC in his last year) to further give him all the leverage in the world. "Pay me what i want or i walk as a UFA in summer of 2024"
What does this even mean? You really think he has any desire or intention to play for LESS on his next contract, for 8 years? Because his next contract will bring him to his mid-30's? Are you contradicting your previous point? I'm honestly not sure.
His next contract will be his biggest potential earning years in the league. Zero chance he gives up even one penny to help with the salary cap mess Dubas put this team into.