No, if the input key has enough entropy then using an MD5 hash will not reduce the security of AES. And AES protects the retrieval of the key from any combination of plaintext and ciphertext. MD5 can be seen as a poor man's (Key Based) Key Derivation Function or KDF which extracts (compresses) the entropy found in the input key material.
However, a lot of times MD5 is used instead of a Password Based Key Derivation Function or PBKDF (bcrypt, scrypt, PBKDF2 and the newer Argon2 variants are well known PBKDF's). If the input is a password or text then it is likely that a low amount of entropy is present. In that case it is easy to guess the input of MD5. The resulting AES key may seem secure and randomized, but the adversary may guess the input - for instance by using a dictionary attack - and perform the MD5 calculation to retrieve the AES key.
MD5 has been broken and the usage of MD5 is a red flag, often indicating that the developer hasn't got a clue about cryptography. This is true regardless if MD5 is used in a secure setting or not. The use of MD5 is often not by design, but because the developer copied another bad example of cryptography. In your case, the MD5 hash is hex encoded and then used as 256 bit key. Although using 128 bits (max) of entropy as 256 bit key doesn't break AES in practice, it does show that the developer wasn't a cryptographer himself.
If the quality is that bad, you can almost be certain that other errors have been made. In your example code, CBC mode could be used directly to achieve transport security, making padding oracle attacks a distinct possibility.
Please learn at least the basics of encoding and cryptography. Whatever you do, don't use self-made protocols like the one in your question. Try and use higher level frameworks or transport protocols such as TLS instead. You have been warned - and it is good you asked.