Answer
the x-axis, the y-axis, and the origin.
Work Step by Step
Step 1. To test symmetry with respect to the x-axis, replace $(x,y)$ with $(x,-y)$, we have: $5(-y)^2+5x^2=30$ which is the same as the original, thus it is symmetric with respect to the x-axis.
Step 2. To test symmetry with respect to the y-axis, replace $(x,y)$ with $(-x,y)$, we have: $5(y)^2+5(-x)^2=30$ which is the same as the original, thus it is symmetric with respect to the y-axis.
Step 3. To test symmetry with respect to the origin, replace $(x,y)$ with $(-x,-y)$, we have: $5(-y)^2+5(-x)^2=30$ which is the same as the original, thus it is symmetric with respect to the origin.
Step 4. Thus the equation has a symmetry with respect to the x-axis, the y-axis, and the origin.