Synthetic natural gas (SNG) production through direct air capture (DAC) and renewable hydrogen could be a potential solution to address the scarcity of natural gas resources, reduce CO2 emissions from the atmosphere, enable the storage of renewable energies, and improve sustainable production. In this study, a renewable grid- connected SNG production system is analyzed, based on DAC technology and green hydrogen as input feedstock, to meet the natural gas consumption needs of a specified-scale residential application year-round. This energy system incorporates a wind farm as a renewable energy supplier to support hydrogen production and CO2 absorption in the methanation process for a residential application in Sankhast city, North Khorasan, Iran. The aim of this research is to present significant findings regarding the implementation of such a system in Iran, assisting engineers in testing and applying it under real conditions. To analyze the system dynamically from energy, exergy, exergoeconomic, economic, and environmental (5E) perspectives, Aspen Plus and EES software were utilized for modeling and simulation. Additionally, the TOPSIS method, a multi-criteria decision-making approach, was employed to perform multi-objective optimization of the SNG production process and the capacity of renewable wind power. The results revealed that the system produced high-quality SNG with 98.7 % methane purity while addressing SNG shortages during peak months by storing excess SNG produced during hotter months, with the highest storage capacity of 13.5 km3 reported in July. Furthermore, the system achieved energy and exergy efficiencies of 31.17% and 18.1 %, respectively, and sold the highest excess power of 1240 MWh in July. In the economic analysis, the highest cost was attributed to investment, with the levelized cost of energy (LCOE) reported at 8.65 $/kWh, where the purchase of wind turbines represented the largest expenditure. Finally, environmental analysis reported that the system could potentially reduce CO2 emissions by 1540 tons annually.