John 5:10 — The Jews therefore said unto him that was cured, It is the sabbath day: it is not lawful for thee to carry thy bed.
11 — He answered them, He that made me whole, the same said unto me, Take up thy bed, and walk.
12 — Then asked they him, What man is that which said unto thee, Take up thy bed, and walk?
13 — And he that was healed wist not who it was: for Jesus had conveyed Himself away, a multitude being in that place.
14 — Afterward Jesus findeth him in the temple, and said unto him, Behold, thou art made whole: sin no more, lest a worse thing come unto thee.
15 — The man departed, and told the Jews that it was Jesus, which had made him whole.
16 — And therefore did the Jews persecute Jesus, and sought to slay Him, because He had done these things on the sabbath day.
The Jews (Jewish leaders) didn't care that the man was miraculously healed, only that he carried a blanket on the sabbath. The 39th and last rule in the tradition of the elders (man-made, not from God) was that nothing could be carried on the sabbath.
Nehemiah 13:9 and Jerimiah 17:21 mention carrying loads on the sabbath, but both refer to merchandise.
conveyed Himself away (v. 13) — to avoid attention and popular admiration. His moving away may have been done miraculously as in Luke 4:30.
lest a worse thing come unto thee (v. 14) — Likely, the man's affliction was the result of a sin he had indulged in.
I think the elders knew who Jesus was and that they were upset, not that He broke the sabbath but, that He revealed that their rules and their "holiness" was hogwash.