I assume the question is whether the vector b is a linear combination of v₁ and v₂. If it is, then that means there are scalars c₁ and c₂ such that
b = c₁ v₁ + c₂ v₂ ==> (7, 4, -3) = c₁ (1, 2, -5) + c₂ (2, 5, 6)
This gives the system of equations,
c₁ + 2c₂ = 7
2c₁ + 5c₂ = 4
-5c₁ + 6c₂ = -3
which has no solution, since
-2 (c₁ + 2c₂) + (2c₁ + 5c₂) = -2(7) + 4 ==> c₂ = -10
but substituting this into any two equations in the system gives contradictory results. For instance,
c₁ + 2c₂ = c₁ - 20 = 7 ==> c₁ = 27
2c₁ + 5c₂ = 2c₁ - 50 = 4 ==> c₁ = 27
-5c₁ + 6c₂ = -5c₁ - 60 = -3 ==> c₁ = -57/5
This means that b is not a linear combination of v₁ and v₂.