Steve Koonin was there in 1988 when the Hawks met the Boston Celtics in the Eastern Conference semifinals, a series that would become punctuation for all of the franchise’s “What-if” debates.

“It was exhilaratingly deflating,” said Koonin, the Hawks’ CEO.

Exhilaratingly deflating.

Could there be a more perfect word pairing to describe postseason history for Atlanta sports franchises?

“When Georgia died on the 5-yard line against Alabama, when the Falcons’ season ended at the same place against San Francisco, when Jim Leyritz hit the home run against Mark Wohlers,” Koonin said, recounting some of his personal agonies as an Atlanta sports fan.

One step from a national championship game for Georgia. One step from a Super Bowl for the Falcons. Two wins from a World Series for a Braves, who would fizzle after sweeping two games in New York.

Exhilarating. Deflating.

The Hawks have teased us this year. They were a joy to watch in the regular season and have been maddening at times in the playoffs. But their last-second win over the Washington Wizards in Game 5 of the Eastern Conference semis Wednesday night shook Philips Arena and the city.

With the series tied 2-2, the massive nuisance, Paul Pierce, made a 3-point shot to give the Wizards a 81-80 lead with 8.3 seconds left. But on ensuing possession, coach Mike Budenholzer called a play for Dennis Schroder to drive to the basket against John Wall. Wall blocked the shot, but Al Horford wrestled Washington’s Nene for the rebound and put home the winning basket with one second left.

Deflating .. then exhilarating.

A positive word reversal.

The Hawks need to win one more game to accomplish something they’ve never done since leaving St. Louis: Win two playoff rounds. They’re 0-13 in the second round in Atlanta and 0-19 since St. Louis won the league championship in 1958. (The second round was the finals in two of those seasons and the Western Conference finals in six of the years, including two in Atlanta.)

The Hawks have never played in the Eastern Conference finals. They came closest in the classic Dominique Wilkins-Larry Bird matchup in 1988, when they won Game 5 in Boston to take a 3-2 series, only to lose the next two. The Celtics won Game 7 in the old Boston Garden 118-116. Wilkins finished with 47 points, including 16 in the fourth quarter; Bird totaled 34, including 20 in the fourth.

That year was the last and only time the Hawks led a second-round series 3-2, before this week.

It would be difficult for any of today’s Hawks to relate to their fans’ lingering torment. Jeff Teague was born two months after Game 7. Horford and DeMarre Carroll were 1-year-olds. Paul Millsap was 3, Kyle Korver 7.

Budenholzer, who was finishing high school in Holbrook, Ariz., at the time of Wilkins-Bird, understands why fans and media are focused on the franchise being on the verge of punching through the ceiling. But he said that can’t be the Hawks’ focus.

“I think for our players and our coaches, there’s a lot of respect for the history and the team here,” Budenholzer said Thursday. “But no matter where you are, there’s a certain degree of that, and people are focused on that. But the players on those teams have to be focused on that moment. Some organizations have won a bunch, but those teams have to focus on what’s going on. We’re trying to keep our focus on getting a win and trying to play a great defensive game. Everything else is out of our sphere.”

One more win would constitute a major leap for the franchise. There already has been significant progress in the product and the brand. Wednesday’s game drew an Atlanta TV rating of 11. Equivalent: 345,000 viewers, the most watched game in Atlanta Hawks’ history. That’s more than triple the average viewer count for games this season (about 100,000) and close to five times last year’s average (70,000).

Obviously, nobody in the organization wants to think about this round ending badly, least of all Koonin. He sat in the stands alone during Game 6 in Brooklyn when the Hawks closed that series.

“It’s the first time I cheered out loud in years,” he said. “Normally I just sit there quietly. Had a great time. I even caught a Brooklyn shirt when they were shooting them out of the (T-shirt) gun.”

He gave it to a young fan. A Nets shirt couldn’t be his favorite memory of the playoffs.