Hmm i don't understand your method at all ha! There should be no eV/s it should be in J/s.
OK here goes ill try and explain it, try and do it my way because i think its more intuitive :). Watts = the amount of joules evolved per second. First part to realize which you got. Secondly 1eV=1.6E-19 joules of energy. How many eV of energy does one photon have in this case?? 2.5eV! SO therefore the amount of energy in joules that one photon has in this case is 2.5*1.6E-19. That will be a MINISCULE amount like E-19. NOW this laser thing is pumping out 0.5 joules per second. How many photons is in that amount of energy?? Just divide 0.5 joules by that number you get for the energy of a photon. And youve got the number per second.
Now REMEMBER this because it is so cool and once you get good at it you can bomb through these questions like nothing. Look at the units of the thing your loking at. In this case we want s^-1 because its photons PER SECOND. We do not want joules so cancel out the joules while keeping s^-1. So like this watts are Js^-1, eV are in J we just did watts/eV which =(Js^-1)/J, oh and look we canceled out the J and are left with s^-1(aka per second). Trying to get to the right units at the end will almost always work. If you look at your attempt it ends up with J^-1 s^2 as its units, that aint going to give us the answer.