with RSA encryption, how do I find the md5sum of the private key from the public key? This is a purely mathematical question on RSA encryption.

Having $e$ as the public key exponent and $n$ the modulus of a public key. Can I recover the md5sum of the private key $d$ (inverse of $d$ according to the modulus.)

Thanks for your help.
You cannot get a hash over the entire private key if you've just got $n$ and $e$. You can however create a hash over the modulus $n$. This is sometimes used as identifier for keys within a key pair, e.g. in PKCS#11. Usually SHA-1 is used however, not MD5.

The modulus is unique for RSA key pairs and links the public key and private key together.

md5sum is a GNU utility that performs MD5, it's not an algorithm in itself.