Yes, 5x5 for bench is PLENTY.
Your diet isn't overly impressive. I doesn't look like you're getting many carbs at all, nor good fats (unless I'm missing something). Your protein intake is also pretty low. Whole eggs aren't so high in protein, maybe 12 grams per 100 grams net weight. If you're taking out the yolk it'll be even less.
Look, I'll be blunt: you're getting good advice from people who started where you did but have advanced. Along the way I'm pretty sure we've all made a bunch of dumb mistakes with training and diet.
So, if you think you know what you need to do, go ahead and good luck. Just remember that you came here asking for advice, which means you probably felt like you didn't know what to do.
You may not like the advice you're getting. That's fine. Doesn't mean its bad advice though.
You've trained for three months and gone from a 60 kg bench to an 80 kg bench. Good. Now it's gotten harder to get stronger. That's normal.
So: do the program set out above. Do it properly. Don't fuck around and add or remove things. Forget the 'I need more volume' crap for three months. Eat a bunch more, and stop wasting your yolks.
Three months later if you haven't put more on your bench and added some muscle into the bargain, THEN you can come back and tell us how it didn't work.