Neha uses all five digit cards to make the smallest 5-digit number she can. What is the predecessor of her number?

A 5-digit number cannot start with 0, so she puts the smallest non-zero digit, 2, first, then 0, 0, 4, 7: 20047. Its predecessor is $20047-1=20046$. (02047 is not a 5-digit number; 20048 is the successor.)