Great question, one I have heard a lot in the last couple of years, it’s a sensitive subject for some coaches and I’ve certainly see a few ruffled feathers when asking why this will not improve given the massive emphasis on V02max work (exactly in the style you described). Most people report that this kind of work only improves their repeatability but not their 5m power. I believe it is a reasonable request to want your coach to improve this as the compound score in elite cycling uses the 5 minute power as a strongly indicative prediction of one day race performance, (although compound score after 2000 - 3000 kJ expended is likely more specific)
First thing to keep in mind is that there are tiers to this sport, some people are literally just built different, we cannot train to reach the level of Tadej, it’s everything at once raw V02max, Central nervous system, fiber typing and 3 dimensional arrangement of skeletal muscle they all play a big role.
So my best 5 minutes is 500w on the trainer and I’ve done 470 for 5 in a race sim a with a higher normalized power equivalent to attacking sitting on the redline trying to hold off chasers and then having to re-surge in order to stay on once they counter attacks come at the end of the climb.
What I did to improve this is really difficult to parse out because in many ways this kind of effort is not a true V02max effort, what I mean by this is that you have to actually start in a much deeper zone and then hold on at V02max and have that ability to go back and forth. Likely anyone who is doing a tremendous 5 minutes power started out by building the anaerobic power around 1-2 minutes and simply did not stop. It’s a conversion of a strong effort (say 7w/kg for 1 minute followed by periods in which your true V02max with redlined heart rate is like the slowest you will ever go in the interval other than for brief moments).
So think of your 5 minute as a continuation of your best 3 minute and think of a strong 3 minute as the result of many years of training and hard work to extend out your best 1-2 minute and think of your best 1-2 minute as a pure expression of your attacking riding ability.
Mentality is everything, stimulus is part of it, having a good drop ride or a race sim or just the right kind mindset is super important, when I did 500 for 5 on the trainer I was playing some extremely strong emotional queues on myself, think like running through the trenches of ww2 trying to get across the gap between the lines with people counting on you to make it, stuff like that.
In terms of specific training without seeing your full history it is hard to say, generically it’s usually way more z2 overload weeks with proper emphasis on metabolic flexibility to fully maximize aerobic systems training followed by workouts that will make you puke or fail within an inch of your life, trigger asthma you didn’t even know you had, etc. I do 10 minute block with 2 minutes at 6.5w/kg followed by 6 minutes at just below FTP followed by 2 minutes at 6.5w/kg. The purpose of this is to leverage long weeks of z2 training and deliver maximum load to anaerobic and V02 systems. It’s a custom workout so based on your level you can tune it such that the average power across the 10 minutes aligns with where you want to be. Pogacar’s version would surely be closer to 9w/kg for 2 minutes on both ends as I am guessing he could probably beat Jonas’s numbers from the start of 2023 where he was able to do 7.46 for 11 minutes etalon w/kg
