Help a chubie nubie to core-work going into cramps after 5 mins

My friend(female) and I(male) are 61 and 66. We love! doing FB upper-body weight training and kickboxing routines - biking and hiking also - together about 2-5 times per week. We are trying to get started with core workouts. Probably due to our desk jobs, we can't get a good start on beginning core workouts/routines (started and stopped many times).

Our physical activities are intensive 50-75% of the time. But, 10 minutes of moderate intensity of any of the level 3 core workouts (particularly ones that include crunches) are too much of a strain for beginners. We need something that will build us up to that.

(After 5 mins, I go into cramps or spasms just below my last rib or the whole area between ribs and belly button.)

Could 2-3 moves we can do 5-10 minutes 3 times a week be the answer?

What other approaches do you beautiful fitness freaks suggest?