Is it possible to decrypt MD5 hashes?

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Someone told me that he has seen software systems that:

  1. retrieve MD5 encrypted passwords from other systems;
  2. decrypt the encrypted passwords and
  3. store the passwords in the database of the system using the systems own algorithm.

Is that possible? I thought that it wasn’t possible / feasible to decrypt MD5 hashes.

I know there are MD5 dictionaries, but is there an actual decryption algorithm?

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