What is the condition for a signal to be invertible?
By definition, a system is invertible, if there is a distinct output for every distinct input, meaning that the mapping of input points (in your case t) to the output (in your case y) is one-to-one. The function or system like $$y(t) = sin(5t)$$
is not invertible since there are tons of input points which result in the same output point $$(e.g. sin(0)=sin(5pi/5)=sin(5(2pi/5))=sin(5(kpi/5))=0 )$$.