Most stock mouthpieces that come with horns are narrow to medium pieces, and too narrow for a full Jazz sound. Many Jazz players use wider tip openings than a 5. Those who use the narrower pieces (e.g. Stan Getz, John Coltrane) use hard reeds with them. Sonny Rollins, who you mentioned you liked, plays wide mothpieces with medium reeds, and he has been using a couple of mouthpieces over his carreer. In the 50's he played most often a metal Otto Link (around 10), then a Selmer (was it an H?) around the "The Bridge" recording, then he switched to Berg Larsen stainless steel (130/2) and LaVoz medium, which he apparently still plays today. He used several others, like Lawton or Wolf Tayne.
I do NOT recommend you simply copy the setup of any player and expect to sound like him. But I'd encourage you to try a more open mouthpiece than a #5. Remember also, the numbering of mouthpieces is different for different brands, there are comparison charts available in the net (e.g.
http://www.saxgourmet.com/mpfacing.html). For Jazz tenor sax a tip opening of 100-110 would be a medium and a good place to start if you have some experience with your stock mouthpiece. A popular choice for a Jazz mouthpiece is an Otto Link 7* or 8, metal or hard rubber. The metal is available with the regular chamber or as "NY" with a bigger chamber for a fuller and darker sound. I cannot confirm the quality control is as bad as Kosma said, at least not in Europe. I tested and bought a couple of Links over the last two years, all of them were good players right out of the box.
If you switch from your current mouthpiece to a wider tip opening, combine it with a soft reed (1,5 or 2) in the beginning. Practise long tones to build up your breath support and embouchure, then increase the reed hardness step by step until you get the sound you like and the setup that suits you the best (most probably a #2 1/2, #3, or #3 1/2). If you have to work too hard to get a sound, the setup is not the right one for you.
Smaller chambers will give a brighter tone, as Kosma said. A wider tip opening will give you a darker tone, but it can be combined with a softer reed, which then gives a brighter tone than a harder reed. Another variable not mentioned yet is the baffle, size as well as design. Higher baffles (i.e. a narrower space between mouthpice and reed) make a piece brighter and easier to play. But the tone becomes thinner. The curve and evenness of the facing also makes a lot of difference how easy and consistent a piece plays. On
http://www.mouthpieceheaven.com you can learn a lot about mouthpiece terminology and variables. You'll also find a list of setups of popular players there.
There is only one basic rule for mouthpiece choice: Try before you buy!