there is a figure that looks kind of like this:

E6--------------------- E= -0.378eV
E5--------------------- E= -0.544eV
E4--------------------- E= -0.850eV
E3--------------------- E= -1.51eV
E2--------------------- E= -3.40eV

the figure shown above shows the enrgy levels for a hydrogen atom. What is the energy of the photon emitted when the electron in a hydrogen atom drops from energy level E5 to energy level E2?

E=E2-E5 = -3.4-(-0.544)
= -3.4 to .54u
= -2.856 eV

is this done correctly?

No. The energy level of a photon cannot be negative. Difference=highlevelenergy-lowerlevelenergy.

so, how would i write it out?

= -0.544 - -3.40
????????

yes -0.544 - (-3.40) = -0.544 + 3.40

Yes, your calculation is correct. To find the energy of the photon emitted when the electron in a hydrogen atom drops from energy level E5 to energy level E2, you need to subtract the energy of E5 from the energy of E2.

E=E2-E5 = -3.4 eV - (-0.544 eV) = -2.856 eV

Therefore, the energy of the photon emitted is -2.856 eV.