To solve this system of equations, we can expand the expressions on the left side of each equation:

(4x+5)2 = 16x^2 + 40x + 25 = 10y
(5x+4)2 = 25x^2 + 40x + 16 = 10y

Now, we can set the two expressions equal to each other:

16x^2 + 40x + 25 = 25x^2 + 40x + 16

Subtract 25x^2 and 40x from both sides:

16 = 9x^2

Divide by 9:

x^2 = 16/9
x = ±4/3

Now that we have found the value of x, we can substitute it back into one of the original equations to find y. Let's use the first equation:

(4*(4/3) + 5)^2 = 10y
(16/3 + 5)^2 = 10y
(31/3)^2 = 10y
961/9 = 10y
y = 961/90

Therefore, the solutions to the system of equations are x = ±4/3 and y = 961/90.