Defining a Sprint goal

might the fact that it is not possible to define one single Sprint goal be an indication for something else: that Scrum is not suited for this team?

Try asking if the product is suited for Scrum. Is it complex enough to present significant unknowns, which Sprint Goals would then help a collaborative team to address?

Having a team work on some disjoint piece of work is a reality. The way I approach this is to think about the Sprint Goal as a focusing tool for the team. Let's suppose that everything starts going wrong and not all of these little pieces of work can be delivered by the team. What is the most important outcome of the Sprint for the stakeholders? That's your Sprint Goal, and the team focuses on what they need to achieve that. Any other units of work that are deliverable are bonuses.

Thinking about the Sprint Goal in this way may help at Sprint Planning, as well. Instead of disjoint work items taken in order from the Product Backlog, work that is more closely related to the Sprint Goal can be selected. It may be beneficial to have the team working on closely related areas of the product to deliver a slightly more cohesive set of changes or value.

If the team is unable to support the Sprint Goal, then I'd want to dig deeper into how the product is defined and how the team(s) are structured to support that product.

In my team, we support 5 different products that is 5 different product backlogs. So, it is very difficult to set a common sprint goal because the team works “each one in his product”, helping each other with impediments but not working together in the same product. I believe that even if we elect some stories as the Sprint Goal based on the most desirable outcome to the Stakeholders, the team would keep working apart. I really would like to know how to address this issue and successfully set a Sprint Goal.

If team members are working on different products, how is teamwork then evidenced, so value can be maximized? What you've described isn't Scrum, so are Scrum outcomes expected?

Scrum, as it's defined in the Scrum Guide, is designed around a Scrum Team consisting of 1 Product Owner, 1 Scrum Master, and a small group of Developers supporting a single product, where all of the work needed in that product is defined in the Product Backlog. Various scaling frameworks, such as Nexus, LeSS, and Scrum@Scale, provide guidance for multiple teams working on a single product.

The situation that you describe where one team is supporting 5 different products within the same Sprint isn't aligned with Scrum. That doesn't mean that some of the practices won't help. Having a unique Product Backlog for each product, for example, is setting you up for success. However, other practices from Scrum really won't help as much since they aren't designed for your situation.