asked to delay my start date by two weeks to finish notice period, no reply since Monday

Signed the offer three weeks ago and now realize my notice period runs another five weeks past the start date they want. I emailed my recruiter Monday asking to push it back two weeks and haven't heard back since, which is doing wonders for my anxiety. Anyone actually done this after already signing? I keep rehearsing the email in my head, something like "I want to make sure I leave my current team in a good place," but it feels like I'm asking for a favor I don't deserve yet. Did it come off as flaky, or did they not care at all?