The difference between 5w30 and 10w30 motor oil is the way the oil works at 0 degrees Fahrenheit, because 5w oil is less viscous at that temperature than 10w. In general, 5w30 motor oil is recommended when the temperature might go below 0 degrees Farenheit, while 10w30 is used when it's likely to stay above that temperature.
The weight of motor oil is how viscous it remains at various temperatures. In dual weight motor oils, there are two numbers listed. The first, in this case the 5 or 10, indicates how it functions at lower temperature. The second number, in this case the 30, indicates how it works at high temperatures. If you live in extremely cold climates, an even more extreme oil may be recommended, such as a 0w30. However, living in a temperate area with mild winters, it is unlikely to make a difference whether a car or truck uses 5w30 or 10w30.
Most engines will come with a recommended motor oil weight. This can usually be found in the car's owner's manual. Some mechanics recommend a different weight depending on the area in which the car is being used and their own experience. Ultimately, the decision should be up to the owner of the car.