No. 5-hour ENERGY drink has a supplement facts label. Energy drinks that have this kind of label are not eligible.
According to the USDA Food and Nutrition Service, when considering the eligibility of energy drinks, and other branded products, the primary determinant is the type of product label chosen by the manufacturer to conform to Food and Drug Administration (FDA) guidelines:
Energy drinks that have a nutrition facts label are eligible foods.
Energy drinks that have a supplement facts label are classified by the FDA as supplements, and are therefore not eligible.
In general, items that are not eligible for purchase with Supplemental Nutrition Assistance Program (formerly Food Stamp Program) benefits include:
Food products that contain alcohol or tobacco products
Items that are not intended for human consumption (e.g. paper products, pet foods, etc.)
Foods sold hot at the point-of-sale, and
Vitamins and supplements
For more info, see Eligible Food Items and How FNS Determines Product Eligibility for SNAP Purchase pages.