There are more than 5 factors, but here are perhaps the most important ones:
1) Light: Light energy is a crucial component in photosynthesis, as it is the primary energy source of the process.
2) Carbon Dioxide: Another key ingredient in photosynthesis.
3) Temperature: There is an optimum temperature for photosynthesis that varies from organism to organism. Too cold or two hot, and rate of photosynthesis will be lower.
4) Water - Like almost all life process, water is a key component in photosynthesis.
5) Oxygen. A common misconception is that plants only "breathe in" carbon dioxide and expel oxygen. Plant cells actually require oxygen as well in order to function, and thus oxygen is a necessary part of photosynthesis.