Sunflower seeds are a rich source of the healthy mono- and polyunsaturated fats that have been shown to improve heart health, however, they are also a source of saturated fatty acids, an excess of which may lead to increased levels of unhealthy low-density lipoprotein, or LDL cholesterol. The American Heart association recommends that people limit their saturated fat intake to no more than 7 percent of calories, which would be 140 calories on a 2,000-calorie diet. One serving of toasted sunflower kernels contains 1.7 grams of saturated fats, which is equal to 15 calories from fat, since fats have 9 calories per gram. If you ate 5 ounces of sunflower seeds in one sitting, you'd be getting 75 calories from saturated fat, which is more than half of your daily saturated fat limit. This could cause problems if you eat other foods high in saturated fat in addition to sunflower seeds.