Change up to a 10gal tank. 5.5 is a bit small for a BP, even a hatchling.

Get a thermostat ASAP! Herpstat is the tops, but Johnson and Ranco are good if you don't have that much to spend. But you NEED one before you get the snake.

UTH pads (with a thermostat) work fine for heat. Make sure you leave the paper covering the adhesive ON and use foil tape to tape the pad to the underside of the tank, paper side to the glass.

As stated, you need another hide. Those caves are nice, but so pricey. Most of us here use plastic plant pots, cut down to about 3" high with a nice 'tunnel' opening in the side. Cheap and easy.

And tanks can work perfectly with just a little extra work. Insulating back and sides and putting the foil treatment on the screen is all I needed to have consistent spot-on temps and humidity. Good luck!