Find inductor current with Laplace
Your textbook is correct. The inductor is connected in between the Node V1 and ground. It is modeled as a constant current source i(0)/s in parallel with corresponding inductor reactance. Now, Look at the original circuit. The current through inductor = the current flowing between node V1 and ground. In the below laplace model, it is nothing but the sum of two currents: i(0)/s and V1/5s (Kirchoff's Current Law). V1/5s will give you only the transient part of current through the inductor, while their sum will be the total current through inductor at any time t > 0.