John 5:16-18
16 And therefore did the Jews persecute Jesus, and sought to slay him, because he had done these things on the sabbath day.
17 But Jesus answered them, My Father worketh hitherto, and I work.
18 Therefore the Jews sought the more to kill him, because he not only had broken the sabbath, but said also that God was his Father, making himself equal with God.
John says that the Jews sought to kill Jesus because He "said that God was his Father, making himself equal with God". This demonstrates that John believed that Jesus is God.
In context, the hostile Jews accuse Jesus of breaking the Sabbath, and Jesus responds by saying, "My Father is still working, and I also am working" (verse 17). John remarks that in this sense, at least in the minds of the hostile Jews, Jesus was "making himself equal with God". In what way? By claiming eternality? By claiming to be Yahweh? Or by claiming to be God? In verse 17, He clearly distinguishes Himself from the Father, and elsewhere in this book, He directly states that "my Father is greater than I" (John 14:28).
Rather, John says that it was because He had "said that God was his Father". Therefore, He claims "equality" in the sense that He claims for Himself the divine prerogative of determining what is proper work on the Sabbath day for Himself, as the unique Son of God. This is a delegated authority from the Father (John 5:19), and the theme of delegated authority is carried on for much of the chapter (John 5:19-38), where Jesus says, "The Son can do nothing of himself, but what he sees the Father do" (John 5:19), and, "the Father judges no man, but has committed all judgment unto the Son" (John 5:22), and, "as the Father has life in himself; so has he given to the Son to have life in himself; And has given him authority to execute judgment also, because he is the Son of man" (John 5:26-27). The unbelievers present believed that Jesus could not claim such things, but according to Jesus, they were mistaken.
In summary, if John meant to describe Jesus as claiming "equality" with God, and was not merely reporting the assumptions of His accusers, it is not "equality in all respects because He just is God" - which is often how the verse is framed by Trinitarians who use it to support the doctrine of the Trinity. It is instead the exercising of divine prerogatives, which have been granted to Him by His Father, as the rest of the chapter explains.