Trample vs indestructible

The way trample works is the attacking player must assign what would be fatal damage to the defending creature(s), with any remaining damage continuing onward to be assigned to the player.  It is important that only "fatal" damage need be assigned, as it is relevant in these sorts of situations or if the trample creature happens to gain deathtouch.

So to state things as clearly as possible using your example:

The 5/5 trample attacks and is "chump" blocked by the 1/1 indestructible.  Pending no other spells are played and this is the final blocking arrangement, you would proceed into the "assign damage" phase of combat.  You, being the attacking player would be given the choice in how much damage to assign to the defending creature (think of trample as being much like them blocking with more than one creature where you get to choose how damage is assigned).  You would only have to assign 1 damage to the blocker as technically that is all you would need for it to be "fatal" damage, regardless of any abilities the creature has that would prevent said damage.  The remaining four damage could be assigned via trample to the defending player.

Does this make sense?

The reason for the distinction of assigning "fatal" damage is relevant for indestructible, regeneration, other prevent damage abilities (see Fog Bank), and deathtouch.  Note that if the 5/5 trampler were to get deathtouch, they could technically block with 10 toughness across three creatures and you would only have to assign 3 damage (one to each creature) for it to fit the "fatal" damage requirement, allowing you to actually trample through with 2 damage in that scenario.

I hope this helps.  I can clarify more if you still have questions.  Lastly, there's no need to apologize, if you're learning the game and need to ask questions, that's what this forum is here for.