welcome back, aren't you a LS expat?
Most higher end tames, and some lower end ones all go to 5 slots now. They all have different specializations though, depending on starting stats, starting slots, element damage spread, available specials, etc.
most importantly, if you have any legacy pets in your stable, DO NOT train them until you are completely familiar with the system. Many are extremely valuable, and can be made very powerful with the training system, BUT are also easy to ruin if you don't know what you're doing.