It will take the search committee a while to complete the first round of review, and often they don't start immediately after the deadline. So a delay of a few days is normally not a problem.
However, a month is really excessive. If that's how long it takes, I think there's a very good chance that they will finish their first round of review before receiving the letter, which effectively means the letter won't be considered with your application.
And it's a serious concern that this letter is from your postdoc supervisor (if I correctly understand what you mean by "host"). It's generally very important to have a letter from your supervisor in your current position if at all possible, and the absence of such a letter may be interpreted as meaning that your work is so poor that your supervisor refuses to recommend you. Typically, if there is some good reason why you don't have a letter (e.g. your supervisor is incapacitated, or has taken a dislike to you through no fault of your own) then the committee would expect it to be explained in your application and by your other writers. So unfortunately, I think that such a long delay could in fact affect your job prospects.
Unless the professor has some really extraordinary circumstances, this delay on their part seems quite inexcusable. Yes, grant applications are important, but writing letters is part of their job too. It's hard to believe they really can't spare an hour or two, over the course of a month, for something with such a significant impact on another person's career.
So I do think it is worth pressing this person to submit the letter promptly. You could, as Buffy suggests, offer to help them with the application or other work, to help free up their time. I generally dislike the notion that you should have to "bribe" someone to write you a letter, but in this case it might be justified. If you have another trusted mentor in this department, you could also talk to that person, who might have some ideas based on their knowledge of your host, or be willing to approach them on your behalf.
In the meantime, I would also suggest contacting the departments where you have applied (at least those in which you are the most interested), to let them know that a letter from your supervisor will be coming. And if you really can't get your host to hurry up, you might ask one or more of your other writers to draft a supplemental letter to the committees, saying that your host is being slow for no good reason and that your work is fine as far as they know.
I don't think getting a letter from Recommender #5 will accomplish much. This is not so much about the total number of letters, but about specifically having one from your supervisor.