Re: How can I do
Use an opamp. Here are 3 examples. The first one will produce 0V for +10V input and 0V for -10V.
The second produces 0 at -10V input and 4V at +10V.
The third uses the entire 0~5V range, but requires a more unusual reference, which can be built with another opamp and some resistors.
Note that in the last two schematics the reference has to be able to both source and sink current, so probably you will have to use an opamp to build the reference.
As for the opamp offset and drift, it depends on the required resolution of the system. Choose the opamp such that the error will be within the allowable limits.