Hmm, I would have thought the 'strict' definition of high-spin is when a transition metal complex can have more than one possible d-electron distribution (e.g. d4 octahedral); then the 'high spin' form is the one with more unpaired electrons, while the 'low spin' has fewer unpaired electrons.
I agree that weak field ligands mean a complex is more likely to be high spin (this is because the lowered energy gap between the orbitals means it's more energetically favourable to put an electron into a 'higher energy' orbital, instead of trying to put two electrons into a 'lower energy' orbital, as the energy required to do this (the spin-pairing energy) is greater than the energy gap (crystal-field splitting energy).
Well yeah, I made that generalisation because for the purposes of first-year chemistry, it's sufficient. But you're right. High vs low spin configurations are really competitions between the stabilisation of the LFSE and the electron repulsions by being in the same orbital. 'High' spin, literally, would mean pairing as few electrons as possible.
The problem about what you've given there though is that d5 octahedral, if high spin, has only one possible d configuration. In addition, you can have low spin electron configurations in which you can fill the orbitals differently like d4, in which any of the t2g orbitals can accommodate the extra electron.
Of course, things get a bit more complicated when you consider different geometries and introduce ligand field theory