Trying to design a fault tolerant topology. I will be stacking all switches with the appropriate stacking cables, my main concern is if I can use the other SFP ports to create the redundant links between floors?
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You are designing a network with 8 switches. In my opinion, it's a network big enough to invest a bit more in a core switch with more 10GB links. Make a pure star topology with a core (switch 3) connected to each switch trought an etherchannel/port-channel (2x10GBx7 switches = 14x10GB).
If you can't afford a core with 14x10GB, try to get a core with at least 7x10GB. Make a star topology with only one link per switch and get redudancy connecting each switch with another one (should be blocked by STP).
If you are stuck to this Cisco model, you can't do much better. Just try to connect switch 1 to switch 3 directly and switch 5 to switch 7. As a best practice, try to not chain switches.
As an opinion, at least, get a decent switch core ;).
There are a few different ways to handle this problem, but to begin with I'd say you should prioritize the physical topology, then focus on the logical. That setup is pretty scary, if you lose one device, say Switch 3, you'd be losing connection to most of you devices. You should look into a star or mesh topology, try to minimize the number of devices a client has to go through to get to your core devices/services. Once you have looked into a more appropriate physical topology, take a look into Etherchannel, which is just Cisco link aggregation, and possibly Multiple Spanning Tree. Depending on the state of your configuration and VLANs, MSTP might be overkill, but it helps to lessen the blow that you'll take to bandwidth from STP.
I assume you mean the SG500X-48P based on your diagram having 10GB between the switches. The SG500X has enough ports to accomplish your desired topology, and you can use standard SFP ports to suport your fiber connections between floors. Lesser 500 models do not have enough SFP ports to support stacking and fiber interconnections.
Check out the 500 Series Admin Guide for more information on the ports or stacking topologies.