+5V --> Reed Switch 1 --> Reed Switch 2 --> Reed Switch 3 --> Reed Switch 4 --> Laser --> Ground
If I understand that correctly you have 4 switches in series so the laser only comes-on when all 4 switches are on (closed)?
I also tried to make my arduino pin HIGH using the INPUT_PULLUP and ran the wire from between the 4th reed and the laser to the IN pin on a 5V relay board.
Which switch terminal did you connect to?
You shouldn't need a pull-up since the 5V is a "hard" pull-up. You may need a pull-down, but I wouldn't think so.
The connection directly to the laser should go high (5V) when the laser is on and low (0V) when the laser is off. Do you have a multimeter to check that?
If the 5V connection to the laser is power, it should give you a "solid" low when off. If it's an enable or trigger input, there is a chance that there is some other short-duration signal there, but that's unlikely.