Cancer is a disease caused by the abnormal growth of cells in different parts of the body and is one of the top causes of death globally. Microarray gene expression data plays a critical role in the identification and classification of cancer tissues. Due to recent advancements in Machine Learning (ML) techniques, researchers are analyzing gene expression data using a variety of such techniques to model the progression rate & treatment of cancer patients with great effect. But high dimensionality alongside the presence of highly correlated columns in gene expression datasets leads to computational difficulties. This paper aims to propose the use of ML classification techniques- Linear Discriminant Analysis (LDA) & Random Forest (RF) for classifying five types of cancer (breast cancer, kidney cancer, colon cancer, lung cancer and prostate cancer) based on high dimensional microarray gene expression data. Principal component analysis (PCA) was used for dimensionality reduction, and principal component scores of the raw data for classification. Six distinct categorization performance measures were used to evaluate these approaches; RF method provided us with higher accuracy than LDA method. The method and results of this article should be helpful to researchers who are dealing with many genes in microarray data.