I firmly believe that you do not need to add cardio to make it a “cutting workout”. It is much more about maintaining a calorie deficit through your diet. So I wouldn’t worry about the cardio hurting the 5x5. I’d be more concerned about the calorie deficit. The problem you are going to run into is that the 5x5 program is built around standard progression. Most likely you will not have any problems progressing at first as your body adapts to the increased frequency and volume. However as time goes on you will find it hard to increase your weights in a constant calorie deficit. I would say that since you won’t be able to increase the weight you are moving during the cut, choose a program where you can vary the set/rep scheme to adjust intensity.
"Heaven and earth shall pass away, but my words shall not pass away." - Matthew 24:35
"But the fruit of the Spirit is love, joy, peace, longsuffering, gentleness, goodness, faith, meekness, temperance: against such there is no law." - Galations 5:22-23