Conversion from continuous to sampled signal?
You typically write a sine wave as 
$$x(t) = sin(2 \cdot \pi \cdot f \cdot t)$$
where t is time and f the frequency of the sine wave. 

Please note that both time and frequency are physical quantities, i.e. they have values and units. The units need to cancel each other since you can't apply the sine function to a unit

If you want to sample this at $f_s = 5000 Hz$ you simply calculate the value every a time interval $T_s = 1/f_s$. You get

$$x_d[n] = sin(2 \cdot \pi \cdot f \cdot n \cdot T_s) $$

or 

$$x_d[n] = sin(2 \cdot \pi \cdot n \cdot f/f_s) $$

Whether this is "correct" or not depends the ratio of frequency to sample rate and whether this meets the criteria of the sampling theorem or not.