The Last Digit

Last digit of 5^{3000} = 5 \\ 2^{3001} = 2 \\ \therefore 5^{3000} - 2^{3001} = 5 - 2 = \boxed{3} \\ {\text{Note: To find the last digit of 2^{3001} ,make patterns. Divide 3001 by 4, the remainder is 1, so unit digit is equal to unit digit of 2^1 = 2}}

$2^{3001}=2^{1+4k} \equiv 2$ , and $5^k \equiv 5$ .