I would interpret "the fourth and fifth digitsfrom the end" of 42218 and 53953 as being 42 and 53 respectively so the years of birth are 1942 and 1953, not 1918 and 1953. I notice that you then use 218 and 953, dropping the first two digits was that "1918" a typo?

The smallest that m or b can be is 1 so the smallest possible value for 40(m-1)+ b+ 500 is 500. That "218" is impossible. Perhaps this was a male?

40(m-1)+ b+ 500= 40m- 40+ b+ 500= 953 or 40m+ b= 493. Again, the largest that m can be is 12 and 40(12)= 480 so it is possible that m= 12, b= 13. If we were to try m= 11, 40(11)= 440 and 493- 440= 53. The only possible answer is m= 12, d= 13. The birthday is Dec. 13, 1953.