Should I setup the network as following?
Of course you can setup such design. However keep in mind that such design is a bad one. Why? Each link between one switch and another is single point of failure. If the link between S3 and S4 breaks; S5 cannot reach Router, S1, and S2. The same sense applies to link between S2 and S3, link between S1 and S2, and link between Router and S1.
Now to solve the failure link possibility, let me ask you this. How resilient do you wish your network be? How do you like your network design between the followings:
So far, the network resiliency issue discussed is just from the internal network (layer-2) point of view. There are also other issues to think of. The followings are just examples.
1. Redundant Routers
In case one router fails (either hardware or software failure).
2. Multiple ISP
When one ISP goes down or has bottleneck traffic issues, there is still another to load balance. You might want to have the 2nd ISP to use different telco lines (different local loop) that connects your site to theirs.
3. Having UPS (Uninterruptable Power Supply)
In case of power outage, there is still time to make necessary file access, save, or backups.
For further info of network resiliency, check out the following FAQ
»Cisco Forum FAQ »Network Design Tips
»Cisco Forum FAQ »Redundant Link Graceful Internet Load Balance/Failover