A V10 engine is a V engine with 10 cylinders in two banks of five. It is longer than a V8 engine but shorter than a straight-6 engine or V12 engine.
The V10 is essentially the result of mating two even-firing straight-5 engines together. The straight-5 engine shows first and second order rocking motion. Here it should be assumed that the crankshaft with low second-order vibration is used and the first order is balanced by a balance shaft. By mating the straight-5 banks at 90 degrees and using five throws, the balance shafts balance each other and become null. The firing sequence is odd (BMW S85, Dodge Viper, Volkswagen Touareg). Using an 18° split journal crankshaft the firing order can be made even, and the two balanced shafts do not balance each other completely, but are combined into a single very small balance shaft (Lamborghini V10, Porsche Carrera GT). Using a five-throw crankshaft and 72° bank angle the firing order can be made even, and the two balanced shafts do not balance each other completely, but are combined into a single small balance shaft (Toyota 1LR-GUE engine). A 36° degree bank angle and a 108° flying arm crankshaft would allow even firing without a balance shaft and smaller counterweights, but would be impractical.
The V10 configuration is not an inherently balanced design like a straight-6, V-12, boxer engine, or V-8 (ignoring the counterweights) and does still have a small second order rocking motion, which can only be compensated by balance shafts.
Until recently, the V10 configuration was not a common configuration for road cars; a V12 is only slightly more complicated and runs more smoothly, while a V8 is less complex and more economical. For the Lexus LFA, the engineers selected a V10 engine over an equivalent displacement V8 because they could not get the V8 to rev as high as the V10, and over a V12 for its lower reciprocating mass, allowing for more rapid engine response. For Audi in their Audi R8 5.2 FSI quattro, the V10 was a compromise between a V12, which would be too long and suffer more internal friction due to extra cylinders and valves, and a V8 which would be more compact but have larger, heavier pistons and have a lower redline.