1. **State the problem:** Calculate the sum of 4723.30 and 5337. 2. **Formula used:** Addition of two numbers is done by summing their values digit by digit. 3. **Perform the addition:** $$4723.30 + 5337 = 10060.30$$ 4. **Explanation:** Adding the decimal number 4723.30 and the whole number 5337 results in 10060.30 by aligning the decimal points and summing each column. 5. **Final answer:** $$\boxed{10060.30}$$