If you are working your arms to fatigue (meaning you wouldn't be able to do one more repetition of the exercise in proper form), then you should take a day of rest in between workouts. If it's just using light weights with high reps that isn't much of a challenge, you should be fine to do it and then strength train the next day.
There could be a lot of reasons for how you felt- depending on what you ate, how much you had to drink, whether or not you warmed up, cooled down, etc. Are you following any kind of 5k training program? If not, you might want to check out the plans on our site to give you a guide to follow.
Hope that helps,