Oh, god, don't compile from source!
Instead, look a bit further down the curl download page:
and you'll see RHEL5 packages for curl 7.24 and use those instead.
If you really, really need 7.19 specifically, get the SRPM from http://curl.haxx.se/download/ and rebuild it from there. Look at http://wiki.centos.org/HowTos/RebuildSRPM for instructions on how to build from SRPM.
Remember, your first best option is to stay in repo. If that isn't possible, stay in packaging (and be aware that you will be responsible for keeping those non-repo packages up to date). Your last, very very last resort, is to build from source and run
Oh, if you click on the RHEL5 link for curl 7.24, you'll see this text up on top:
The version of curl and libcurl here provides libcurl.so.4, whereas
many distributions include a version of curl that provides
libcurl.so.3 or libcurl.so.2. This means that installing the curl and
libcurl packages from this repository can break a lot of dependencies
for applications linked against the older libcurl. This problem can be
avoided by also installing the libcurl7155 (for libcurl.so.3) and/or
libcurl7112 (for libcurl.so.2) packages, for backwards compatibility
That's how you will deal with, say, php complaining about needing libcurl.so.3.