To determine the interval where the inequality Log5$3x+1$>log5$x-3$ is true, we first need to isolate x by getting rid of the logarithm.

Using the property if log_a$b$ > log_a$c$ then b > c. We can rewrite the inequality as 3x+1 > x-3.

Now, solve for x:
3x + 1 > x - 3
3x - x > -3 - 1
2x > -4
x > -2

Therefore, the solution for the inequality is x > -2.

The interval where the inequality Log5$3x+1$>log5$x-3$ is true is $-2,\infty$.