I'll get you started but I don't want to do your homework. Temperature and polarity of the molecule affects the solubility.
I know that temperature, polarity, and pressure are three of them. I was wonder what the other three are. I thought that maybe it might be stirring and the size of the molecule too. But then that means I'm missing one.
I don't think I can be much help; I don't know exactly what your sources (teacher/text) count. Some factors can be included as one item or broken down into several.
Here is what I can offer.
You have P and T.
Nature of solvent
Nature of solute
presence of common ion
presence of complexing agents/reacting agents. I consider solvation energy as nature solute/nature solvent but others may separate those. Common ion effect falls into the same category in my opinion. I hope you can read through these thoughts and choose those that fit into your guidelines.
I consider bonding (hydrogen bonding for example) to be included in nature of solute/nature solvent. Same for presence of complexing agents or other agents that react with one or the other; if I add another material to increase the solubility I think we have changed the "solution." Lattice energy I consider nature of the solute.
I don't consider stirring one of them because stirring increases the RATE at which dissolution occurs but not the solubility. I don't consider particle size either; grinding a solid into a powder increases the surface area which increases the RATE but not the solubility.