Well, welcome to specificity. For 1RM performance to be optimal you have to train for 1RM's. That's not to say that you can't make a lot of progress on your 1RM by training in 5's or 5x5 or whatever over a period but you won't perform at your potential best and fully realize that progress on your 1RM by just going in and doing it randomly after a 5x5 program. So to fully realize 1RM performance at a given point in time, you have to train for it and 'time' for it assuming a periodized program (i.e. a point of low fatigue rebounding off a previously higher level).
Hopefully this is making sense. You can get a lot stronger in 5's, and it really will translate into a bigger 1RM eventually but if a 1RM is really your barometer you have to train more specifically for it at a given point in time to expect optimal performance. Looking at Westside's ME days, they are using this to keep 1RM style lifting on decent frequency within their program even though the lift itself may not be a competition lift. Looking at the Korte 3x3, the loading period is followed by a deloading period of what effectively becomes practice and maintenance work while the big lifts are geared up week to week - to where a final compeition week and day exist. This gearing up is crucial. The ME days are crucial in Westside's conjugate system. So for the 5x5 you'd have to alter it. Maybe that would be a deloading phase similar to Korte's where a series of singles are done post 5x5 loading. Maybe a phase like that after the 3x3 phase where one has peaked to records and assumably loaded up again (i.e. make sure you do even if you have to add work - this is kind of a personal tolerance but you'd effectively have teirs of deloading where the first phase would culminate in very high fatigue, a breif respite, middle teir would still peak out and keep a moderate amount of fatigue, and then this would disipate as the singles were brought up).
That's an option, if 1RM is really important to you, maybe look more closely at a Westside template which can be altered as needed as it's fairly flexible.
Hope that helps explain why an issue exists and gives some line of thought on how you might handle it if that's something important to you in each phase you do or over a longer period.