Deleting row if all column values are a particular string

Hello,

I have a very large file for which I would like to remove all rows for which the value of columns 2-5 is zero.

For instance I would like this file:
contig1, 0, 0, 0, 0
contig2, 1, 3, 5, 0
contig3, 0, 0, 0, 0
contig4, 0, 5, 6, 7

To become this file:
contig2, 1, 3, 5,0
contig4, 0, 5, 6, 7

I'm aware that you can use 'Awk' to remove rows for which a particular column has a specific value, but I can't seem to figure out how to remove a row if multiple columns have to have a particular value (i.e zero).

Thanks!