Age-related diseases, such as osteoarthritis, Alzheimer’s disease, diabetes, and cardiovascular disease, are often associated with chronic unresolved inflammation. Neutrophils play central roles in this process by releasing tissue-degenerative proteases, such as cathepsin G, as well as pro-inflammatory leukotrienes produced by the 5-lipoxygenase (5-LO) pathway. Boswellic acids (BAs) are pentacyclic triterpene acids contained in the gum resin of the anti-inflammatory remedy frankincense that target cathepsin G and 5-LO in neutrophils, and might thus represent suitable leads for intervention with age-associated diseases that have a chronic inflammatory component. Here, we investigated whether, in addition to BAs, other triterpene acids from frankincense interfere with 5-LO and cathepsin G. We provide a comprehensive analysis of 17 natural tetra- or pentacyclic triterpene acids for suppression of 5-LO product synthesis in human neutrophils. These triterpene acids were also investigated for their direct interference with 5-LO and cathepsin G in cell-free assays. Furthermore, our studies were expanded to 10 semi-synthetic BA derivatives. Our data reveal that besides BAs, several tetra- and pentacyclic triterpene acids are effective or even superior inhibitors of 5-LO product formation in human neutrophils, and in parallel, inhibit cathepsin G. Their beneficial target profile may qualify triterpene acids as anti-inflammatory natural products and pharmacological leads for intervention with diseases related to aging.