multiple subnets within a vlan not allowed?

Assuming your Cisco Gi0/0 interface connects to your F5 1.1 interface, the configuration would look like this (ips/vlans/etc are just examples):

  
  Cisco:  
    
  interface GigabitEthernet0/0.790  
   encapsulation dot1q 790  
   ip address 10.79.0.253 255.255.255.0  
  interface GigabitEthernet0/0.791  
   encapsulation dot1q 791  
   ip address 10.79.1.253 255.255.255.0  
  interface GigabitEthernet0/0.1680  
   encapsulation dot1q 1680  
   ip address 192.168.0.253 255.255.255.0  
  interface GigabitEthernet0/0.1681  
   encapsulation dot1q 1681  
   ip address 192.168.1.253 255.255.255.0  
    
  BIG-IP:  
    
  vlan vlan_1 {  
     tag 790  
     interfaces tagged 1.1  
  }  
  vlan vlan_2 {  
     tag 791  
     interfaces tagged 1.1  
  }  
  vlan vlan_3 {  
     tag 1680  
     interfaces tagged 1.1  
  }  
  vlan vlan_4 {  
     tag 1681  
     interfaces tagged 1.1  
  }  
    
  self 10.79.0.254 {  
     netmask 255.255.255.0  
     vlan vlan_1  
  }  
  self 10.79.1.254 {  
     netmask 255.255.255.0  
     vlan vlan_2  
  }  
  self 192.168.0.254 {  
     netmask 255.255.255.0  
     vlan vlan_3  
  }  
  self 192.168.2.254 {  
     netmask 255.255.255.0  
     vlan vlan_4  
  }  
  

The vlans in this case would be locally significant the router and to the BIG-IP if they are directly connected. If switched, you would need to consider your vlan architecture for such a change.