score:11
There is nothing prohibiting this. The circumstances could easily lead to greater scrutiny, of course. If you are in a position to offer evidence of your plans to leave the US after 5 days, you should be fine. Your air travel booking is of course one part of that evidence (which the immigration officer should have access to without your having to show it). Any appointments you might have in the UK or elsewhere after you leave the US might help. But there's every possibility that you won't be asked for any of that.
Upvote:8
Note that contrary to the Schengen Area for instance, which has a very well defined rule on how long you can stay over a longer period (the 90/180 rule), the US does not have such a rule.
Travellers using the VWP cannot stay more than 90 days in a row (including travel to adjacent countries and neighbouring islands), and they should not be attempting to live in the US. There are no hard and fast rules on how long you must be away before you can return.
A rule of thumb published by CBP is that if you stayed 3 months, you should be away for 3 months before returning, but this is usually taken in the context of βreturning for 3 more monthsβ, or at least a significant duration.
For a short stay (which, as @phoog explained, would be good if it was easy to demonstrate with a return ticket and other evidence), though, this should be fine, especially since there will have been a full month since your last departure.
Be prepared for additional scrutiny, and have as much evidence as possible of your intention (or even need) to depart the US promptly. This is of course much easier if you have a full time job waiting for you rather than being a student on sabbatical or being unemployed.