In the circle AB=19, BC=10, and CD=5. The diagram is not drawn to scale.What is the value of xx=23x=53x=38x=58

we know that
If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

so
BC*AC=CD*(x+CD)
AB=19
BC=10
CD=5
AC=AB+BC----> AC=29
(x+CD)=BC*AC/CD-----> 10*29/5-----> 58
(x+CD)=58------> x=58-CD-----> x=58-5----> x=53