I'm not familiar with the Fortigate 100D, but if you've configured a VLAN interface on that box and assigned it the number 5, the firewall should send and expect to receive 802.1q tagged frames with that specific VLAN number.
If you then connect the physical interface of the Fortigate to a switch port in access VLAN 5, the Forticate will send 802.1q tagged frames labeled "5" to a port which is a member of VLAN 5 and expects untagged frames. That won't work.
Try configuring the switch port as a VLAN trunk with a native VLAN other than 5:
Code:
Switch(config)#interface GigabitEthernet 0/1
Switch(config-if)#switchport mode trunk
Switch(config-if)#switchport trunk native vlan 1
This is assuming that the port in question is "GigabitEthernet 0/1", of course.