I want to use a Red Hat Enterprise Linux RPM software package on CentOS 5.6, but I don't know which version of RHEL works with CentOS 5.6.
RHEL 4 = CentOS 4?
RHEL 5 = CentOS 5?
The version numbers correlate between RHEL and CentOS (as Ben Preston already answered). Moreover, due to RHEL philosophy, the ABI should stay the same across all minor number ( .x) versions, so the package compiled for 5.4 should most likely work for 5.5 and 5.6 as well.
CentOS uses the source packages of RHEL to create the CentOS OS. So OS versions are the same in both the cases. CentOS is the carbon copy version of RHEL with better support for drivers and packages which RHEL cannot support due to its policies. You get a lot of packages from EPEL for CentOS.
You can use a rpm package for CentOS, keep in mind your architecture and your version.