First off you need to head to the goblin village Northwest of Fallidor.
*Note: You will need to bring some food, and also equip the proper armor and weapon (which is steel at this point, black for weapon) if you can afford it. You should start by raising your defense to at least level 20. Then also raise your attack to level 20 as well.
If at anytime you get low on food, be sure to take some time out and visit the bank in Fallidor to buy or take food out of your bank account. When you have reached the desired goals for defense and attack, concentrate on raising your strength to level 25. This should roughly take around 2 hours to complete.
If at anytime you feel that the level 5 goblins are getting hard, or taking too much food, you can always stay at the goblin house Northeast of Lumbridge to achieve your leveling goals.
Congratulations! You have just reached combat level 25.
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