Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.

To determine the nature of the solutions for the given system of equations, we can analyze the two equations:

1. \(-3x + 5y = 5\)
2. \(-6x + 10y = 10\)

First, let's check if the second equation is a multiple of the first. We can multiply the first equation by 2:

\[ 2(-3x + 5y) = 2(5) \ -6x + 10y = 10 \]

We see that the second equation \(-6x + 10y = 10\) is exactly the same as the transformed version of the first equation. This means that both equations represent the same line.

Since both equations are equivalent, they do not provide conflicting information, and therefore, they have infinitely many solutions (all the points on that line).

In conclusion, the system of equations has infinitely many solutions.