What happens if full thrust is applied at cruise altitude for 5-10 minutes on a 787?
Autopilot flying straight and level

Upon reaching the VMO/MMO the A/P will be inhibited from trimming down any further, which will result in the airplane climbing at the VMO/MMO.


  Overspeed protection limits the speed to which the airplane can be trimmed. At VMO/MMO, the trim reference speed is limited by inhibiting trim in the nose down direction.


Hand flying straight and level

Pushing the thrust levers forward will result in a climb at the current speed due to the fly-by-wire design—only the trim buttons change the "trim reference speed".


  Once the column forces are trimmed to zero, the airplane maintains a constant speed with no column inputs. Thrust changes result in a relatively constant indicated airspeed climb or descent.




Source: Boeing 787 FCOM chapters 4 and 9.

Further reading:


What does the term &quot;trimming&quot; most commonly mean in aviation?
Why does overspeed cause structural damage or failure when limit load factors are not exceeded?
How does envelope protection work in Airbus vs. Boeing aircraft?
How does auto-trim work on fly-by-wire aircraft?