HR/Recruiters, how do you typically handle a preferred candidate whose expected salary is on the higher end?

Let's say you found the most perfect candidate for an important role that's currently vacant. Let's call him Person A. He is very experienced, he is capable, he got all the skills and talents you asked for. Just perfect. There are also Person B who is kinda good, and Person C who is just okay.

The salary range advertised for the position is $4,000-$5,000.

What if, Person A asked for $5,000? Do you give him the offer, or do you negotiate for a lower salary?

What if, Person A asked for above $5,000? Maybe $5,500 or $6,000? Do you consider raising the salary range or do you go ahead with Person B and C instead?

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