To solve this system of linear equations, we can use the substitution method or the elimination method. Let's use the substitution method:

Starting with the first equation:
5x + 2y = 1.25

Solve for x:
x = (1.25 - 2y) / 5

Substitute x into the second equation:
2((1.25 - 2y) / 5) + 3y = 1.05

Expand and simplify:
(2.50 - 4y) / 5 + 3y = 1.05
2.50 - 4y + 15y = 5.25
11y = 2.75
y = 2.75 / 11
y = 0.25

Now substitute y back into the first equation to solve for x:
5x + 2(0.25) = 1.25
5x + 0.50 = 1.25
5x = 0.75
x = 0.75 / 5
x = 0.15

Therefore, the solution to the system of equations is x = 0.15 and y = 0.25.