What kind of foundation do you have? If it is a monolithic concrete (single structure with no joints) then I wouldn't worry about it. If it is block, brick or rock, then there is the potential for roots to get into cracks in the structure and begin to enlarge them.
How deep is the foundation? If it's a slab, then you could get roots growing under the foundation and lifting, however if you have a 7' deep foundation, it is unlikely the roots will go that deep.
It looks to me like the soil around the trunk of the tree is too deep, as there is no root flare.
My concern about a tree planted that close is not the foundation, but rather the gutters and roof edge. You need to prune the tree so that it wont damage the gutters and roof edge when (not if) it sways in the wind.
As noted above, I would suggest you consider removing the tree in the long term before it damages your house (foundation, siding, roof or all three).
Just remember, we or an arborist who comes to your house, is giving you advice, suggestions, observations or recommendations. You are the ultimate decision maker. An arborist who comes to your house cannot order you to remove the tree.