We just bought a house in December and in the last month or 2 have had to cut down multiple dead trees and have seen serious signs of concern for another 6. They aren't all the same type of tree, and are showing 2 sets of symptoms. We have asked around and the type of trees and issues have been unable to be identified. We need help before the problems worsen and/or spread.
If you have had multiple trees die, it's possible that either the problem is cultural--such as construction occurred near and over the roots of many trees--or many of them were ash trees and died from the invasive emerald ash borer insect. Many ashes are currently dying from this foreign pest. No ashes will survive. You can search emerald ash borer on our website.
Your two trees, however, should be fine.
Your first tree shows something called 'slime flux', which doesn't usually hurt trees at all. This explains what is happening: https://extension.umd.edu/hgic/slime-flux-and-wetwood-trees-and-shrubs
The second photo shows a tree with holes made by sapsuckers, a type of woodpecker that makes the holes to reach insects and sap. There can be hundreds of these holes, and trees are able to tolerate them. No action is necessary. Read here: http://extension.umd.edu/hgic/woodpeckers-and-sapsuckers
If you would like to know what kind of trees you have, send us photos of the leaves.
We'd be glad to id them.