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**HallsofIvy** You can use those angles to find the horizontal and vertical components of the force. If $\displaystyle T_1$ is the tension in the string that makes 53 degrees with the horizontal the the horizontal component of force is $\displaystyle T_1cos(53)$ and the vertical component is $\displaystyle T_1sin(53)$. Do the same with the string that makes the 37 degree angle.

Obviously, depending on the which string is on the right and which is on the left, one of the horizontal forces will be positive and one will be negative- it doesn't matter which you take positive. Both vertical forces will be upward. The sum of the horizontal forces must be 0 and the sum of the vertical forces will be the weight of the mass, 5g Newtons (NOT 5 kg- that is not a force). That will give you two equations to solve for $\displaystyle T_1$ and $\displaystyle T_2$.