The datasheet for your module is somewhat minimialist, but it does include these lines.
There are two ways to read this:
The laser module contains no internal current regulator. You should use a controlled current source providing 25-35 mA. The regulator will need to provide about 3.0 V to produce this current. If you provide more current, the laser output will be brighter. I think this interpretation is less likely because in this case they should have given a "max" value for the operating voltage, but it's hard to trust such a minimal datasheet.
As you say, your laser module could contain an internal current regulator. You should not be driving it with 5 V, you should be driving it with 3 V as specified in the datasheet. You do not need a current limiting resistor, the internal regulator will limit the current to about 25 and no more than 35 mA. You have no control over how bright the laser operates.
In this case, if you really want to use your 5 V supply to drive the laser, rather than use the 3.0 V supply specified, you need to reconsider the resistor values you are using.
You need the 5 V, minus the resistor drop, to be about 3 V. That means you need 2 V drop across your resistor at 25 mA. That means you need about 80 Ohms, not the 200-1000 Ohms you were working with.
Be aware that if you are wrong, and there is no internal current regulator, it will be pretty easy to damage the laser by biasing it incorrectly. Exceeding the 35 mA max current spec for even a microsecond could permanently damage the laser. A proper fixed-current source is strongly recommended in this case.
Edit In reply to your comment, if you use a fixed-current regulator, it won't increase its output voltage any more than it has to to produce the current you set it to produce. If you make a 25 mA fixed-current regulator, and the device only needs 3 V to draw 25 mA, the regulator won't produce more than 3 V.
A simple fixed-current regulator can be made from a '317 regulator:
You'd adjust R1 to reduce the output current to 25 mA. However this would actually require something like 7.5 V at VIN to ensure it can regulate properly. With a modern low-dropout linear regulator you should be able to make a similar circuit that can produce regulated 25 mA at about 3 V load voltage from 5 V input.