If a Boeing 707 hits turbulence that registers as +5 G on the FDR, would the 787 experience lower G forces due to the flexibility of their wings?
The 787 will not experience lower G-forces, it will experience them later. If the turbulence is of short duration, the 787 might not register much while a 707 is shaken thoroughly. If the updraft persists, both aircraft will eventually feel the same forces.

When an aircraft enters turbulence, the wings experience more lift and start moving upwards. If the wings are heavy (full tanks) and floppy, it takes quite a while before the fuselage experiences any forces. After the wings reached their upper bending limit, the fuselage starts moving upwards together with the wings. In an aircraft with lightweight, stiff wings, the fuselage follows any wing movement immediately.