Is F5-Fortinet full mesh setup will work even without switch?

Yes, it will work Earwin but as future perspective if your ports on F5 & FGT gets over-subscribed/over-used & you want to connect other box as well with F5 or FGT hence switch is needed between them effectively. Also your FGT is active/active & 1 F5 is active so both FGT traffic will go to 1 F5 only so take care of it bit no doubt F5 is intelligent & scalable/reliable device (depends on hardware)