10.5#17

I know that to find the angle I have to use the formula a DOT b =
|a||b|cos(theta). For my two normal vectors I get <5,-5,1> and <2,3,-4>.
This leaves theta = cos^-1(-9/sqrt(1479)). I get 103.53 degrees or 1.807
rad. What did I do wrong?

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OK, it's true that the angle between two planes is the angle between their normal vectors, the question is which normal vector of the plane do you use, because there are two opposite directions that are normal to a given plane.  Here is a representation of the two planes, all arrows are perpendicular to a plane, the black arrow is perpendicular to one plane and both the red and blue arrows are perpendicular to the other plane. You can see that the blue arrow has an obtuse angle with the black arrow, i.e. more than 90degrees, which has a negative cosine, while the red arrow has an acute angle with the black arrow hence the cosine is positive.  This is reflected in the fact that the two planes have two different angles between them, one less than 90degrees and the other greater than. BY DEFINITION though, the angle between the two planes is taken to be the smaller.  SO: to compute the angle between the two planes, you get to use the normal vector that makes the dot product positive.