Esther's First Banquet
When Esther goes in to see the king, he is receptive to her—she would not die. Xerxes knows that she must have some important reason for daring to approach him, and he reassures her of his favor, promising her up to half his kingdom—“probably an example of Oriental [i.e. Middle Eastern] courtesy that was not intended to be taken too literally (cf. Mark 6:23 Mark 6:23And he swore to her, Whatever you shall ask of me, I will give it you, to the half of my kingdom.
American King James Version×)" (Expositor's Bible Commentary, note on Esther 5:3 Esther 5:3Then said the king to her, What will you, queen Esther? and what is your request? it shall be even given you to the half of the kingdom.
American King James Version×).
Esther's response is not to immediately plead for her people. Instead, she invites the king and Haman to a banquet she has prepared for that day. Given the presumptuousness of her entrance, she may not have deemed it a good moment to compound the problem by possibly upsetting the volatile king in revealing that she, his wife and queen, had for all this time not disclosed her national identity to him. It could also be that she did not want to reveal this matter before all the royal officials who were probably present. But why invite Haman to the banquet? "Many suggestions have been made. To make Xerxes jealous. Perhaps so that Haman's reaction, when Esther accuses him, might reveal his guilt. Perhaps Esther acted in the best traditions of her people, to confront Haman face-to-face rather than speak behind his back" (Bible Reader's Companion, note on verse 4).
Xerxes realizes that Esther did not risk her life for a mere banquet. And he probably understood that she prepared the banquet so as to avoid discussing the real reason before all of his officials. At the meal, then, the king asks her for her actual petition. But she delays, asking the two back for a second banquet the next day—which, remarkably, the king does not question. "One may ask why Esther waited instead of disclosing what was on her mind. [Whatever her reason,] the delay providentially allowed time for the king's sleepless night and the events that followed (ch. 6)" (Nelson Study Bible, note on verses 6-8).
Haman's brief exultation is cut short by Mordecai's disrespect (verse 9). His vanity caused him such hatred for Mordecai that he could not enjoy how well things seemed to be going for him (verses 10-13). Of course, in this case things were not going so well as he thought. "Haman's boasting only accentuated his later humiliation and fall from favor (cf. Proverbs 16:18 Proverbs 16:18Pride goes before destruction, and an haughty spirit before a fall.
American King James Version×)" (Expositor's Bible Commentary, note on Esther 5:11-12 Esther 5:11-12  And Haman told them of the glory of his riches, and the multitude of his children, and all the things wherein the king had promoted him, and how he had advanced him above the princes and servants of the king.  Haman said moreover, Yes, Esther the queen did let no man come in with the king to the banquet that she had prepared but myself; and to morrow am I invited to her also with the king.
American King James Version×).
The "hanging" proposed for Mordecai was, as the Word in Life Bible points out in a note on Esther 2:23 Esther 2:23And when inquisition was made of the matter, it was found out; therefore they were both hanged on a tree: and it was written in the book of the chronicles before the king.
American King James Version×, "probably not hanging as we know it. The gallows of ancient Persia was not a scaffold but a pole or stake upon which the victim was impaled. Execution by such impalement was a common practice of the Assyrians, who killed war captives by forcing their living bodies down onto pointed stakes. The Persians continued this grim means of execution. Thus references to hanging in Esther (Esther 5:14 Esther 5:14Then said Zeresh his wife and all his friends to him, Let a gallows be made of fifty cubits high, and to morrow speak you to the king that Mordecai may be hanged thereon: then go you in merrily with the king to the banquet. And the thing pleased Haman; and he caused the gallows to be made.
American King James Version×; Esther 6:4 Esther 6:4And the king said, Who is in the court? Now Haman was come into the outward court of the king's house, to speak to the king to hang Mordecai on the gallows that he had prepared for him.
American King James Version×; Esther 9:14 Esther 9:14And the king commanded it so to be done: and the decree was given at Shushan; and they hanged Haman's ten sons.
American King James Version×) probably refer to impalement, or possibly crucifixion."