First, you should understand what sprints are for. Sprints were introduced as one of methods which helps teams to limit amount of work being done in a specific time. In sprint we commit that we're going to finish a bunch of tasks in some time -- 2 weeks in your case.
However sprint isn't the only method of limiting work in progress. Another concept which deals with the same issue but differently are limits introduced by Kanban. In this case you just limit haw many tasks can be in progress in any given time and you don't introduce cadence for your production cycle.
In both cases the goal is to avoid big chunks of project being started and not completed, even though concepts are different.
Now, coming back to your question: there are teams which typically work with a week long sprints and they're perfectly fine. The style of work is pretty much the same as with 2 week long sprints. It does mean however that they're working on pretty small tasks as they're able to build, verify and deploy features in a week. From this perspective 5-day long sprint isn't that different -- if your tasks are small enough it may work.
On the other hand 2-day long sprint is a sort of extreme. I don't know any team that is doing such short sprints on a regular basis. My question would be: what is so important that you don't want to wait till the end of the week? Note: I consider a week long sprint as an alternative here.
If you just have to deliver under such short deadlines, e.g. you have SLAs or you focus on maintenance projects, that don't really suit your regular sprint schedule you may reconsider having sprints at all. Some elements of Kanban (limiting WIP, no time-boxing and visualization) can be a better approach in such situation.
A few things you may want to take into consideration:
- How fluent the team is with the current process. The more smoothly things work, the less you should rush to introduce huge change.
- How often there is a need to have this unusual sprint. If the anomaly happens every now and then you should think on rearranging your process. On the other hand if it happens twice a year you can probably live with it.
- How much current process is adjusted to the specifics of work you do. For example, time-boxing-based approaches aren't the best tools if you deal with a lot of maintenance work.
Answering to these questions should help you to decide whether short sprints are the way to go or maybe you should reconsider using time-boxing.
And the last final advice: a bit of experimenting with your process is always a good thing.