3 equations in 4 variables

Pardon my ignorance but can SINGULAR find for me the number of intersection curves through the origin of three varieties in 4 variables given by three polynomials whose lowest degrees are 3,5,5 resp.? The higher degree terms of the three polynomials are of degree only one or two more than these lowest terms. Of course parametrisations of the intersection curves would be even better but for now I am content with knowing how many, say their tangent vectors at the origin.