# Where can I look up some Schubert calculus numbers?

I don't know much about Schubert calculus, but I would like to know all of the intersection numbers $$\#(X_{w_1} \cap X_{w_2} \cap X_{w_3})$$ where $X_w$ indicates a Schubert variety (maybe translated) in $\mathrm{GL}_5/B$, $w_1, w_2, w_3$ are in $S_5$ and $w_1 w_2 w_3$ is the long element of $S_5$.

There are a priori too many such numbers to fit in a table (medium-sized fraction of 120^3), but maybe there are some symmetries and redundancies that cut it down?

Failing that, is there some computer code that will tell me all of these numbers?

A package to compute intersection numbers in Macaulay2 is Schubert2 (which has its full documentation here). Sage has a similar package, and a forthcoming implementation called Schubert3.
I haven't used it, but the documentation for the Sage package lrcalc suggests it can do this, and even gives an $Fl(5)$ example.