First, you need to know what the voltage is currently. ( it is a 12 volt battery )
For that, you will need a multimeter set to DC and 20 volt range or autorange if it has it. ( you can get one from Autozone or Advance - about $24 )
If the reading is real low, like 2 volts or so, you probably won't be able to charge it, you'll have to replace it.
The trickle charger / maintainer you have is fine, it just won't charge the battery very fast, it's not meant to.
As to why it went dead after 5 weeks, I would say that's normal without a maintainer connected.
To use your maintainer, connect the red ( plus ) lead to the plus battery terminal ( the one closest to the firewall ) and the black lead to the other terminal.
BTW, when removing a battery, it's always negative off first, and when reinstalling, it's negative on last.