It is an automatic transmission with 5 forward gears.
In addition to the stated number of gears, an automatic transmission will usually have an extra overdrive gear. For example, a 4-speed auto will have a 5th overdrive gear. In the case of my car, my 3-speed auto has a 4th overdrive gear. Overdrive usually does not engage until about 45 MPH. However, some older cars do not have an overdrive gear.
More gears allow shorter shifts for faster acceleration, which is useful in smaller engines with less low-end torque. The less gears there are, the larger the ratios. Overdrive allows the engine to travel as high speeds while maintaining a low RPM for lower fuel consumption.
"Automatic" means that the transmission shifts gears by itself and operates on a torque converter.