I've currently been testing out a Weyland 7-Agenda 5/3 deck. Because I'd have seven agendas either way, I do have one Oaktown in there... (Really useful if I have a 5/3 in my hand to bait a run out first and then IAA the 5/3 right after...) Weyland does have a unique reason to run 5/3 in Public Support, because I only need to score twice, and Support will give me the win. Because it's 7-agenda, there's not much reason to run GFI in it. I still need 3 scores, and so does the Runner, unless literally all three steals were GFI.
I've found High-Risk Investments to be a very useful Agenda to defend against Account Siphon. Once it's scored, I'm perfectly happy to let you double my money for me. Government Contracts similarly lets me not worry about Siphons... The deck loses out of R&D and Remote, so it doesn't like to ice HQ much at all. Those two agendas let me avoid icing HQ as long as one of them is scored.
However, this deck is a bit of anomaly. If you aren't going for minimum agenda density while still being score-able (Government Takeover...) then non-TFP 5/3's are going to be worse than GFI.