You: I don't know, you're in a much better position to judge my worth to the firm than I am.
Decisionmaker: But in terms of an actual number?
You: [Polite nothings. Repeat as necessary.]
Decisionmaker: Alright, how would $80k do?
You: That's interesting. Would you do $85k?
Decisionmaker: OK.
That is literally how simple it is, and your downside risk is "Alright, in that case, $80k is alright" and nobody will remember this conversation 2 weeks from now except your checking account. You can do more complicated things, like demonstrating value to the firm, or treating any no as a suggestion that you negotiate some other aspect of the offer instead, but the simplest way to improve outcomes at negotiation is to actually negotiate.
The marginal $5k gets compounded at every annual raise you have, virtually certain to be calculated by an HR drone's spreadsheet by multiplying a contentious number by a very non-contentious number (your current salary -- now $5k larger). It will increase other benefits you receive, such as employer match to your IRA. If you actually treat questions about salary history at face value when switching firms, it will also act as an anchor for your pricing for the rest of your career. (Giving out salary history? Yeah, that's another thing that can't possibly help you. Anyone asking you for salary history is saying, in as many words, "Please give me a reason why I should give you less money.")
