I think the biggest problem when trying to make 5/3s better (without designing new ones) is avoiding making the 3/2s stronger at the same time. Which would make the change quite pointless.
So far we have quite a lot of cards that provide interaction with agendas.
You can split them in three main categories: Fast advance, protection, and punishment. You could add a 4th category called bluff and list the other cards in there that can be advanced.
Fast advancing is great if it works, but the tools are most useful for 3/2s, etc. Scoring 5/3s using fast advance is pretty much restricted to combo decks.
Protection in form of other cards like Ash, Caprice, etc helps 5/3s but also helps the 3/2s. Only the effects that are tied to the agenda itself, i.e. TFP and GFI are really helping in that regard.
Punishment in form of Midseaon Replacement doesn’t care which agenda is stolen and if you want to build a deck around it you usually want to have more agendas instead of less, making it boost decks with more 3/2s instead of 5/3s. Punitive is the only card that really has an impact when it comes to 5/3s in this category.
So what can be done in the different areas without actually printing new agendas?
Fast advance - One idea I have is a to make a card that allows fast advance tied to the advance requirement of the agenda. For example an event: Cost X. Double. Place X-10 advance counters on an agenda, with a maximum of counters based on the advancement requirements of the agenda -1 or 4 whichever is lower. Sure it is expensive but it does allow to fast advance a 5/3 and it is pretty much pointless to fast advance a 3/2. (The numbers obviously need some tweeking…)
Protection - We already have a current that forced the runner to play 2 credits if he wants to steal an agenda. An upgrade or current that would base the cost on the advancement requirements would benefit the bigger agendas, too. To avoid a pile of upgrades one could always print on the card that it cannot be rezzed if another upgrade is rezzed in the server.
Punishment - More operations that base the punishment on the point value or the advancement requirements of the stolen agenda. Be it number of tags, amount of credits destroyed, number of cards moved of archives to HQ or R&D, extra clicks gained. There are a lot of options. Basing the punishment on the number of agenda points in the runners score area is another option. We already have cards that base punishment on the number of agendas in the runners score area, why not more variety there?
Overall, I think there is quite a lot of design space left to have a meaningful impact on bigger agendas. At the current time though, I don’t see any reason to play any other 5/3 then GFI or TFP.