You have more than 1 problem. This has nothing to do with the sputtering (Glider addressed that issue). This info applies to the B1005 DTC only.
There are two wires going to the fuel level rheostat. A black and yellow/white. If you put an ohm meter across those 2 wires and run the float level up and down, you will probably find an open spot where the meter reads something greater than 260 ohms.
A full tank reading should be between 39.5 and 27.5 ohms on the rheostat. An empty tank reading should be between 260 & 240 ohms. A B1005 DTC is set when the speedo sees an empty tank reading greater than the 260 limit for more than 15 seconds.
Keep in mind that a break in the wire, a poor connector contact, or even a poor ground (the black wire at the rheostat is ground) will tell the speedo the same thing as the rheostat being above the 260 limit. When I say 260 limit, I don't mean if the reading is 261 you have a bad rheostat because these rheostats are not that precise. I would be looking for a something above the 300 range even though the spec is nothing greater than 260.
Try clearing the code 1st. If it returns, address the problem. If you happened to turn on the ignition when the sending unit was removed, a B1005 would set.