Find the GCF (greatest common factor) of the following terms. \[ \left\{5 x y^{2}, 25 x^{2}, 15 x^{2} y^{2}\right\} \]

Step 1 ：The GCF of a set of terms is the largest term that divides all of the terms in the set. To find the GCF, we need to find the common factors of all the terms. In this case, we need to find the common factors of \(5xy^2\), \(25x^2\), and \(15x^2y^2\).

Step 2 ：We can see that 5, x, and y^2 are common factors in all three terms. Therefore, the GCF is \(5xy^2\).

Step 3 ：The GCF of the coefficients is 5, the minimum power of x is 1, and the minimum power of y is 0. Therefore, the GCF of the terms is \(5x^1y^0\), which simplifies to \(5x\).

Step 4 ：Final Answer: The GCF of the terms is \(\boxed{5x}\).