What does it mean to be "equal with God" in John 5:18?

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John 5:18 (ESV):

18 This was why the Jews were seeking all the more to kill him, because not only was he breaking the Sabbath, but he was even calling God his own Father, making himself equal with God.

The concept of equality with God is stated in the verse but not defined. Equality in what sense? Is there any way to infer what the author meant by equality with God from the context? Was the concept of equality with God known to the Jewish leaders who wanted to kill Jesus?

I believe that elucidating the meaning of the expression is a key first step in order to answer other closely related questions, such as:

• Did Jesus deny equality with God in John 5:19 in an attempt to clarify the Christological misunderstanding of the Jews who wanted to kill him?
• How do we reconcile John 5:18 with Psalm 2:7?
• John 5:18 — John’s own Christology or Misunderstanding of the Jews?
• In the Gospel of John, did the Jews disbelieve or misunderstand the Lord Jesus Christ?