I'd steer clear of Multimailer for an one-off blast like this. their delivery isn't awful, but the reputation risk on a fresh domain isn't worth it. With 5K clean leads, you're sitting on a solid list, but sending even 500 emails in a day from a new domain will get you flagged by most major providers.
Here's what I've seen work for an one-time send without burning the domain:
Warm up the domain first - even if it's just for 10-14 days. tools like Mailwarm or Warmbox can ramp up from 10 to around 100-150 sent per day. Then you're ready for the campaign.
Use a dedicated Sending Platform - something like MailerLite, SendGrid (via API with a subdomain), or even a lean tool like Sendinblue. Multimailer is more for ongoing sequences and variable insertion, not a single clean send.
Segment by engagement risk - split that 5K into tiers: leads from the last 6 months, then older ones. Send the newer group first, wait 72 hours, then the rest. That way you don't trip spam filters with a sudden 5K spike.
Set proper SPF, DKIM, and DMARC - sounds basic, but I've seen people skip it and then wonder why they land in promotions or spam.
Send from a subdomain - like mail.yourdomain.com, not the root. Protects your main domain's reputation if you take a hit.
If you already own Multimailer and are comfortable with it, you could rig it to send capped batches (like 200/day for 25 days), but that defeats the "once" part. For a single blast to a clean list, I'd pick a platform that handles bursts better, not one designed for drip campaigns.
Out of curiosity - why the need to hit everyone at once? if it's time-sensitive, you can always use a tool like Lemlist for a short sequence with a single follow-up, then pause after that. Less risk of burning the domain if you stop after one round.