The present work evaluates the effects of different solar radiation values (350, 400, 650, 900, and 1000 W/m²) and module temperature on the monocrystalline solar module output current, voltage, and power. A five-parameter model was chosen to design a simulation program to study and analyze the effects of irradiance and temperature on the output power of a solar module. Solar modules are defined by electrical factors like open circuit voltage, short circuit current, maximum power, maximum current, and maximum voltage, that not supplied by the manufacturer. The proposed work is suggested for the accurate determination model of a mono-crystalline solar module. Ideality factor calculation is by using the mathematical function, Lambert W function and series, and shunt resistances lead to extracting solar module parameters. The fitness of the five-factor formula is related to the lower RMSE average values. The average root mean square error of measured current-voltage values with the corresponding calculated values by the five-parameter model was calculated (0.0667). The lowest value of the root mean square errors of measured voltage-current characteristic values with the calculated ones is 0.022 at irradiance of 1000 W/m²  and module operation temperature of 25 °C. Certainly will enhance the present work's fitness, represented by measured data or calculated model data with RMSE equal to 0.0667. It noted that the present work is so close to other important previous work, and that certainly enhances our work fitness (represented by measured data or calculated model data) with a 0.46 percentage of power drop per degree centigrade.