Network virtualization enables 5G slicing, a technique for sharing physical resources among isolated slices managed by different actors. However, monitoring slices' performance is becoming challenging due to the significant network overhead associated with direct measurements. To overcome this problem, we propose using network tomography to estimate slices' delays in the network. In particular, we investigate the problem of finding the minimal combination of end-to-end simple monitoring paths needed to minimize the estimation error of the slices' delays in a network. We proposed a new genetic algorithm to identify the optimal monitoring paths required to achieve network tomography and minimize their number. To improve the search for the optimal solution, we investigated both a fixed mutation approach and our proposed adaptive mutation approach. Our evaluations show the effectiveness of both approaches; however, the adaptive mutation method outperforms the fixed method by exploring new solutions and avoiding local minima, leading to faster convergence and better results.