Radar used to upgrade F-4 and Kowsar are very similar,one used for Kowsar is probably smaller and considering that I saw MFDs and radar on F-4 I know for sure that they can integrate Fakour and PL-12 or any other modern missile,new multipurpose radars are digital and there is no limits in terms of integration.From F-4 MFD I saw it is clear what capability radar have but unfortunately I think Kowsar would be limited to only one such heavy missile to carry under fuselage but that would mean it had to fly without external fuel tank...I didn't check,but I'm not sure can F-5 carry 500kg under wings....Total payload of F-5 is not issue,but I don't know max weight it can carry on wings...Any way, when it comes to new radar,they can integrate any missile...that is why only modernized F-4 carry anti-ship missile...like noor or qadr,these missile have similar guidance as active guided a2a missiles,active radar + mid curse correction/ins but aircraft needs multipurpose radar like we saw on upgraded F-4 and Kowsar...So,they can put one Fakour under fuselage but range would be restricted to Kowsar radar range+active seeker on missile...I'm not sure is one long range missile worth to produce adapter and external fuel tank...It is more effective to just add 2 F-14 to fly in same formation...So yes it looks like impossible for someone who doesn't know anything about...Reason why F-14 was only capable fire aim54 in that time was because F-14 was only aircraft with sami-digital radar and what AWG-9 gives capability to simultaneously fire to 6 targets is RWR/RWS ,today every multipurpose radar(including one we saw on F-4)is capable for different mode of operations, that is why we can see RWR,CV,T-Pulse ..etc in MFD of F4...and that is why these radars are multipurpose... With standardized signal processing...there are no limits...that is why you can see 3th of khordar fire Sayyad missile...and that is why old air defense systems are digitalized...for easy integration, better resistance, multi channels
I checked F-5 wing payload ,it is 650kg/sq meter so it has sufficient payload to carry 2 Fakour 90 on wings + more weapons or fuel and just because there is no picture it doesn't mean anything, we didn't see picture of Kowsar armed with anything....But there would be more effective to add PL-12...we will see,truth is Iran has F-14,MiG29,F-4,F-1 and Kowsar would be more effective for R-73,short range interception and for CAS missions