The most damage a Lv. 5 Rogue with 2 daggers (I'll be generous and give him 2 daggers) is doing is 2d4+3d6+DEX ( =1d4 dagger +1d4 dagger +3d6 Sneak Attack). With 16 DEX that's 18.5, and that's the ceiling (barring a crit).
The base damage a Lv. 5 Fighter with a greatsword (plus Great Weapon Style) is doing is 4d6(r1&2)+2*STR. With 16 STR that's 22.7, already surpassing the maximum of what the Rogue can do. Oh but I didn't even add the Great Weapon Master feat yet. That's another +20, making the Fighter's damage ceiling 42.7. Oh, I didn't Action Surge? I did now. 85.4. What about a few Superiority Dice? That'll be another 4d8 to the damage ceiling, or 18 more points.
So "Conan" here, at Lv. 5, can choose a round to inflict a maximum of 103.4 points of damage. Even if the Fighter misses on 2 of his 4 attacks on his Action Surge turn (likely if he doesn't get advantage), he's still dealing more than 50. All the dagger guy will ever do in comparison is 18.5 at most. Ever.
Clearly, you did not think this comparison through.