+1: You receive these whenever you help a neighbor, however you can send these to all of your neighbors and when the gift is accepted by your neighbors one will be returned to you as well from each person that accepts the gift. You may send one gift a day per neighbor, 30 at a time but you may repeat this action periodically.
example: if you send out 30, & all 30 are excepted you will receive 30 back. (located in your backpack) after you accept the request.
+3: You receive these from helping your neighbors as well. Since this is my personal observation, I'm not sure as to what specific tasks you help with that will give you the +3 (still researching)
+5: You can craft the +5 by using 8 Goodwills, 7 Loves, & 3 Buzzes. These are items you receive from interacting with other sims, in conversation, doing a good deed around their house, & even flirting with them. Also you may want to hold off on crafting the fun potion & inspired potion, because it takes Love & Goodwill to craft them as well.
Another item in your backpack you may want to take a look at is the cleaning collection which you can craft using 4 Cloths, 4 Gloves, & 4 Dusters. These items can be retreived by rummaging trashcans, & cleaning things around your house & even a neighbors home. Using this item will give you +3 energy as well as 150 simoleons.
Another way to gain energy is to visit your neighbors. Whenever you visit someone you recieve five bonus energies, if you use all five bonus energies you recieve the gift of +1 energy. If it's your first visit you recieve + 3.
However you can also purchase energy with simcash, +10 costing you 9 sim cash, & +15 costing you 12 sim cash.