(1) Background: Cancer stem cells (CSCs) are a subpopulation of cells in a tumor that can self-regenerate and produce different types of cells with the ability to initiate tumor growth and dissemination. Chemotherapy resistance, caused by numerous mechanisms by which tumor tissue manages to overcome the effects of drugs, remains the main problem in cancer treatment. The identification of markers on the cell surface specific to CSCs is important for understanding this phenomenon. (2) Methods: The expression of markers CD24, CD44, ALDH1, and ABCG2 was analyzed on the surface of CSCs in two cancer cell lines, MDA-MB-231 and HCT-116, after treatment with 5-fluorouracil (5-FU) using flow cytometry analysis. A machine learning model (ML)–genetic algorithm (GA) was used for the in silico simulation of drug resistance. (3) Results: As evaluated through the use of flow cytometry, the percentage of CD24-CD44+ MDA-MB-231 and CD44, ALDH1 and ABCG2 HCT-116 in a group treated with 5-FU was significantly increased compared to untreated cells. The CSC population was enriched after treatment with chemotherapy, suggesting that these cells have enhanced drug resistance mechanisms. (4) Conclusions: Each individual GA prediction model achieved high accuracy in estimating the expression rate of CSC markers on cancer cells treated with 5-FU. Artificial intelligence can be used as a powerful tool for predicting drug resistance.