Fig 4 of the datasheet shows switching of an AC signal. If your input signal goes to -5V then the negative supply terminal (Vss) of the IC must be more negative, e.g. -6V.
No, that will not work. For Vin = off, you have to be less than 30% of Vdd-Vss (5 - -5 = 10, @ .3 = 3V, above vss = -2V with respect to ground... the data sheet shows 2V above Vss for guaranteed low).
However, fig 18 of the data sheet shows you can use a 4054 with Vdd = 5V and Vss =0V and Vee = -5V, and uses a 0-5V switch input to turn the 4066 on and off. This looks exactly like your application.