Poisson distrubtuon

Ok so your given 2 distrubution X-po(2) and x-po(3) for a 5 minute period
Pass a certain pint
Now I want to find the probability that there,s at least 1 car in each direction that will pass that certain point in a 2 minute period
For this I worked the total probability of at least 1 car passing by doing 1- probability of 0 cars going in a 2 minutiae period so 1-0.135=0.865 but the answer is wrong and my book says it,s 0.5947. So where did I go wrong?

It helps to upload the full question. but at least 1 in both directions is
1 - (none in both directions + 1 in direction one & 0 in direction two + 0 in direction one & 1 in direction two)