You have only part of the information, and have managed to get the cart ahead of the horse.
Tohatsu motors are not identified by year of manufacture, but rather by precise model/serial. The MFS4/5/6 came out around 1998, and is still in production. The 5A models came out before the B models, and those of course before the C models. So... "old" is relative. You have one of the earlier copies of the MFS5, which originally came with the 3H6032000 carburetor. The part numbering system is constantly being updated, and today, 3H6032000 is superceded to 3R1032001M. This carb also came on the 5A2. Of all carbs for the MFS5 available today, this is the best-performing, most reliable version of carburetor. In later years, the B (and now C) models have been released, in order to accommodate EPA emissions regulations. The newer style carbs interchange directly with the older carbs, so yes, you could put a newer style carb on the A series motor. But, given the option, I would always recommend the earlier-style carb for reasons of overall performance and reliability.
Yes, the most common problems on these motors are fuel-related... so the vast majority of repairs on these is to the carb... BUT... that does not mean that a competent mechanic should just jump into a repair without doing at least some diagnosis. If in fact you are suffering from a too-lean condition, particularly at low speeds, you are probably headed in the right direction by addressing the carb.
Why do you have a new fuel pump? Did the original one test bad? A bad/marginal fuel pump will normally limit top speeds, not idle speeds.
Did you attempt to clean the carb? If so, what method did you use? What did you do to "try" to rebuild it.
In the US, in over 85% of problems like yours, we find that the carb is suffering from varnishing in the low-speed and/or idle passages. This kind of varnishing, since it is inside the passages, is not visible to the ***** eye. It is also very resistant to garden-variety spray-can carb solvents. If you are convinced that you are running too lean at low speeds, you should clean the carb properly and thoroughly. If you did not do a full disassembly of the carb (including jet and emulsion tube nozzle), then submerge the non-rubber bits in real carb dip such as Tyme, for approximately 4 hours at room temperature, followed by a blow-out using generic carb spray, and then a careful reassembly, paying attention to float height, you would want to do that. There are no shortcuts here; "Mechanic in a Can spray" will not be aggressive enough to do the cleaning I am describing.
If you are unsuccessful with the cleaning... and are still sure that you are starving for fuel... and that the rest of the fuel system is good... you can replace the carb. If you are considering that option, you could increase your horsepower by 20%, by installing the carb for the 6A2. It is a direct interchange. The 5A is a de-tuned 6A; The de-tuning is accomplished by using a smaller carb on the 5 hp model. In that case, you could order 3R4032001M CARBURETOR ASSY, MFS/NSF6A2, $116.52, from any dealer, including me.
To reduce the occurrence of this kind of varnishing in the future, be certain to religiously run the carb dry at the end of each and every day.
