Higher mass stars will have shorter lives. Even though they have more fuel for nucleosynthesis, they burn this fuel much quicker than lower mass stars.
Generally, you should think of "red-giant" as an evolutionary phase and not a particular type of star.
Looking at the Scheller et al. (Aston. Astrophys. Suppl., 96, 269, 1992) data given in one of the comments, you want to compare the times denoted by points 5 and 6: ascent of the (first) red giant branch. For a one solar mass star, the elapsed time ascending the giant branch is 634 million years. By comparison, the time for the same phase for a five solar mass star is 0.289 million years.
When looking at the Hertzsprung-Russell chart (surface luminosity vs effective temperature), the RGB tracks at lower masses are all bunched up. Therefore, it is very difficult to discern stellar mass (and age) from just luminosity and temperature. By looking at chemical composition through spectroscopy, it is possible to infer mass by the different types of nucleosynthesis.