I have attempted to add the VLAN manually into the switch with no favorable result, however based upon your recommendation I will try again. I had thought that with the Sophos firewall configured for VLAN51 and with the vSphere portgroup configured for VLAN51 that the Cisco managed switch would just serve as an intermediary and allow communication between the two devices.
This leads me to something that has confused me: you can see from the PNG that VLAN2, VLAN3, VLAN4, VLAN5, VLAN50, VLAN 52, AND VLAN 53 are all present. However I have configured no VLANs for those numbers. I did configure VLAN 50 at the firewall and statically assigned my ESXi host and vCenter Server static IPs in the .50.* subnet, but never did I do any configuring in the firewall for VLAN 50 other than to explicitly assign Gi0/17 and Gi0/19 those VLANs. I suppose perhaps the original owner of the switch may've had those configured; that's the only thing I can imagine would cause those VLANs to appear.
So to follow your instructions, I will create VLAN51 in the Cisco switch. That's easy enough. But to your knowledge, will I need to do anything to add it to my trunk ports? As I understood it, trunk ports carry all VLANs by default unless specific VLANs are defined. Thank you for your help thus far.