A healthy tree close to a house is an asset. A failing one is a roof claim waiting for the right thunderstorm. The good news is that trees almost never fail without warning — they just give the warning quietly, usually for a season or two before anything happens.
Start at the bottom. Mushrooms or shelf fungus growing at the base, or anywhere on the trunk, mean the wood inside is already being digested. The canopy can look completely fine while the structural wood at the base is gone. This is the single most under-read warning sign we see, because the tree looks green and nobody thinks to look down.
Then look at the soil. If the ground on one side of the trunk is heaved, cracked or lifted, the root plate is moving. On a pine that has started to lean after a wet spring, that is not settling — that is the beginning of a failure, and it does not reverse.
Look up for deadwood. A few dead twigs are normal. Large dead limbs still attached, bark falling off whole sections, or a crown that leafed out noticeably thinner this year than last all say the tree is losing ground. A thinning crown two years running is a tree in decline.
Finally, look for cracks and included bark where the trunk splits into two main stems. A V-shaped union with bark pinched down inside it is far weaker than it looks, and those are the failures that take half a tree off in a storm. Sometimes that can be cabled rather than removed, which is worth asking about before anyone quotes you for a takedown.
None of this means the tree has to go today. Plenty of what we look at just needs deadwood taken out and weight reduced. But any of these five on a tree that could reach your house is worth a free look from someone who climbs them for a living, and we would rather tell you it is fine than take out a tree that did not need to come out.