Right off the bat, we can notice that Angle ABD is a right angle. This means that it must add up to 90 degrees. Therefore, we can write that:

Let's combine like terms:

Solve for x:


Now, since we need to find the measure of angle ABC which is given by (5x+3), we can plug the newly found value of x in to figure it out:

Therefore,
Angle ABC = 53°.