As per my knowledge,Peap uses TLS protocol also to authenticate.
PEAP works in the following way:PEAP operates in two steps. The first step is the server authentication and second one is user authentication using a new EAP type .
PEAP uses TLS to authenticate the network infrastructure through the TLS Handshake protocol, to protect user credentials in transit by means of the TLS Record Protocol, and to generate cryptographic keying material using the TLS-defined pseudo-random function (PRF) functionality.
Basically, EAP-MD5 and PEAP are totally different in the backend. PEAP uses server-side certificate to authenticate the server, after which uses user's login name and password for authentication of the client.
EAP-MD5 only authenticate the client without the server authentication part.