This paper compares the ability of three‐factor and five‐factor asset pricing models to explain the apparent profitability of a broad selection of anomalies in Australian equity returns. Rather than examining the fit of each model to common test portfolios, our focus is on the spread return to long–short trading strategies designed around so‐called anomalies. After documenting significant spread returns to 16 anomalies (including several not previously studied in Australia), the empirical analysis provides cautious support that the recently‐proposed investment and profitability factors have a role to play. The number of anomalies that remains after risk adjustment decreases under the five‐factor model. Further, while the magnitude of reduction in alpha is modest, our testing shows that it is statistically significant in many cases. However, both three‐factor and five‐factor models repeatedly fail the Gibbons, Ross, and Shanken's (1989) (GRS) test, suggesting that the quest for a better asset pricing model is not yet complete.