You still have at least a week to improve your season high rank.
It’s been awhile since the Season 4 of Competitive Play started in Overwatch. As you might have expected, it will come to an end and it will happen this month. As for now, we all have to wait a bit longer for the specific date.
The info was confirmed by Game Director Jeff Kaplan, who told users on Blizzard forums that Season 5 is expected to start “around the first of June”. There’s usually a few days of pause between seasons, so we expect the current one to end in two weeks time at most.