Step 1 :The number 5.03 is not a natural number, whole number, or integer because it is not a whole number.
Step 2 :The number 5.03 is a rational number because it can be expressed as a fraction.
Step 3 :The number 5.03 is not an irrational number because it can be expressed as a fraction.
Step 4 :The number 5.03 is a real number because all rational and irrational numbers are real numbers.
Step 5 :\(\boxed{\text{The number 5.03 belongs to the sets of rational numbers and real numbers.}}\)