Calculating the energy of a hydrogen atom

[Benzoate]

Homework Statement

A sample of hydrogen atoms are all in the n=5 state. If all the atoms return to the ground state, how many different photon energies will be emitted , assuming all possible transitions occur?

Homework Equations

possible equation: E= hc/lambda =(E(initial) -E(final)) .
1/lambda = R*(1/m^2-(1/n^2))

The Attempt at a Solution

Not sure where to begin on this problem, but I suspect I should find the energy of the hydrogen atom between the transitons of the two state. I know n=1 for the ground state.

1/lambda=1.097*10^7*(1/1^2-(1/5^2))

Not sure how to find the Number of photon energies :(

 

[Benzoate]

why hasn't anyone answer my question

 

[learningphysics]

Wouldn't you just have 1 possible transition for every 2 states... so using combinations wouldn't the answer be 5 choose 2?