If hashing algorithms such as MD5 or SHA1 both use Merkle-Damgard constructions at their cores, why is it so easy to break them, and yet so much harder to break SHA3, which is also MDC based?
MD5 and SHA-1 have been broken (from a collision-resistance perspective) due to weaknesses of their compression function, not because they are Merkle–Damgård based.
SHA-2 hashes (SHA-256, SHA-512..) are Merkle–Damgård based, but use more compute-intensive compression functions, and are so far unbroken.
SHA-3 is not Merkle–Damgård based, it uses the sponge construction. One advantage is that the result does not reveal the full state, and that makes the construction immune to the length-extension attack.