Given the patient is suffering from muscle spasms.
The mass of Valium to be injected to the patient suffering from muscle spasms =4 mg
Given the bottle of valium with a density of 5 mg/mL
We know that, Density = 

Volume = 

Mass = 4 mg Valium 
Density = 5

Calculating the volume from mass and density:
Volume of valium to be injected
 =0.8mL
=0.8mL
Therefore, a volume of 0.8 mL of valium is to be injected to the patient.