The forward voltage of a diode is dependent on the current. Most datasheets include a graph that show forward voltage versus forward current. The forward voltage of normal silicon diodes is between 0.6V (low current) and 1.2V (high current).
If you need a stable voltage, then a diode is not an optimal solution if the current varies. However, you normally see 0.6V..0.8V drop within reasonable bandwidth of current.
You do need to have a diode that can cope with the current. It needs to have a higher max. forward current rating than that you's need. The second thing is that you need to get away with the power dissipation. A diode with 0.7V forward voltage and 2A of current dissipates 1.4W and that becomes heat.
The diode you mention, 1N5391, has a forward voltage of 0.86V..0.95V at 0.5A (just under 0.5W dissipation at those parameters). The thermal properties are Rja = 60 deg/W, so you will see about 30 degree increase above ambient temperature if you just put it in.