Just from the view alone, I'd say the two are definitely too close to the house. Especially because they are so large, this would be very concerning. Mold and roof repairs are the first problems that come to mind among others. Good Luck!

Buy the house, get the trees cut down, and get professional landscaping.

Yes they can be cut down easily, but not cheaply. It will be a couple thousand dollars for those 2 trees.

price depends on the value of the wood which a good tree service will credit back to you. we had two giant oaks taken down for truly cheap. big pines, expensive!