Here's the '84 Tigers game by game record.
https://www.baseball-almanac.com/teamstats/schedule.php?y=1984&t=DET
- The Tigers were 30 games over .500 after their first 40 games of course, at 35-5
- They then played the next 40 games at .500, as they were 30 games over .500 after their first 80 games, at 55-25
- But by 100 games in they were 38 games over .500
- At the 3/4 of the season they were back down to 35 games over .500, at 78-43. So after the 35-5 start they played the next half of the season, 81 games, at just 5 games over .500 (43-38, .530, 86 win pace). That's the closest I can see to "played .500 ball after the 35-5 game start"
- Then they turned it on again and finished the season 46 games above .500, having played the final 1/4 in 26-15, .634, 103-win pace