"Older Landmark tiller with a 5 HP motor", this sounds as if it may have a Briggs & Stratton horizontal shaft motor where the gas tank is located under the carb. IF SO: there is a diaphragm located on the side of the carb which will go bad just sitting around for a short period of time. This little rubber diaphragm is the fuel pump, pulling fuel from the tank and pushing it into the carb. Do yourself a favor and purchase a repair manual for you brand and HP motor. There will be an entire chapter on carbs which will most likely show this set-up. A new diaphragm will cost under $2 and will make a world if difference in this motor's performance.