How does dependent origination and the skandhas fit together? I’m having trouble seeing whether the idea of the five skandhas is meant to fit within dependent origination in any way, or whether the two theories  are meant to be applied as complements to each other. 

Is there a sutta elaborating on the correlation between the two of them? (Please note that my question primarily regards suttas that addresses the relationship between the two, instead of  details of either concept).
Dependent origination is about the origination of suffering (sorrow, grief, despair, etc) that comes from ignorantly attaching to the khandhas as 'self' ('upadana') and as 'a being' ('jati'). Not only is attachment itself a mental state fraught with anxiety &amp; stress, but the sorrowful traumatic idea of 'aging-&amp;-death' occurs when the khandhas attached to as 'self' or 'a being' are inevitably subjected to impermanence. SN 12.66 says: 


  ‘The many diverse kinds of suffering that arise in the world headed by aging-and-death: this suffering has acquisition as its source, acquisition as its origin; it is born and produced from acquisition. When there is acquisition, aging-and-death comes to be; when there is no acquisition, aging-and-death does not come to be.’


The word "acquisition' ('upadhi') above is a synonym for 'attachment' ('upadana'). SN 12.66 is one of many suttas that shows the word 'jati' in Dependent Origination does not mean 'physical birth'. Instead, 'jati' ('birth') means 'identifying' with something as 'self', 'mine' or 'a being'. MN 26 says: 


  And what may be said to be subject to birth? Spouses &amp; children are subject to birth. Men &amp; women slaves... goats &amp; sheep... fowl &amp; pigs... elephants, cattle, horses, &amp; mares... gold &amp; silver are subject to birth. Subject to birth are these acquisitions, and one who is tied to them, infatuated with them, who has totally fallen for them, being subject to birth, seeks what is likewise subject to birth.


For a more simple explanation of how attachment to the khandhas results in suffering when the khandhas change due to impermanence, SN 22.1 says:


  "Now, how is one afflicted in body &amp; afflicted in mind?
  
  "There is the case where an uninstructed, run-of-the-mill person — who has no regard for noble ones, is not well-versed or disciplined in
  their Dhamma; who has no regard for men of integrity, is not
  well-versed or disciplined in their Dhamma — assumes form (the body)
  to be the self, or the self as possessing form, or form as in the
  self, or the self as in form. He is seized with the idea that 'I am
  form' or 'Form is mine.' As he is seized with these ideas, his form
  changes &amp; alters, and he falls into sorrow, lamentation, pain,
  distress, &amp; despair over its change &amp; alteration.
  
  "He assumes feeling to be the self, or the self as possessing feeling, or feeling as in the self, or the self as in feeling. He is
  seized with the idea that 'I am feeling' or 'Feeling is mine.' As he
  is seized with these ideas, his feeling changes &amp; alters, and he falls
  into sorrow, lamentation, pain, distress, &amp; despair over its change &amp;
  alteration.
  
  "He assumes perception to be the self, or the self as possessing perception, or perception as in the self, or the self as in
  perception. He is seized with the idea that 'I am perception' or
  'Perception is mine.' As he is seized with these ideas, his perception
  changes &amp; alters, and he falls into sorrow, lamentation, pain,
  distress, &amp; despair over its change &amp; alteration.
  
  "He assumes (mental) fabrications to be the self, or the self as possessing fabrications, or fabrications as in the self, or the self
  as in fabrications. He is seized with the idea that 'I am
  fabrications' or 'Fabrications are mine.' As he is seized with these
  ideas, his fabrications change &amp; alter, and he falls into sorrow,
  lamentation, pain, distress, &amp; despair over their change &amp;
  alteration.
  
  "He assumes consciousness to be the self, or the self as possessing consciousness, or consciousness as in the self, or the self as in
  consciousness. He is seized with the idea that 'I am consciousness' or
  'Consciousness is mine.' As he is seized with these ideas, his
  consciousness changes &amp; alters, and he falls into sorrow, lamentation,
  pain, distress, &amp; despair over its change &amp; alteration.
  
  "This, householder, is how one is afflicted in body and afflicted in mind.


We should study the whole of SN 22.1 thoroughly until we understand it clearly. SN 22.1 is spoken in simple language and is not rocket science. 

All of the above is reflected in the most brief explanation of Dependent Origination, from MN 28, below: 


  Now this has been said by the Blessed One: “One who sees dependent origination sees the Dhamma; one who sees the Dhamma sees dependent origination.” And these five aggregates affected by clinging are dependently arisen. The desire, indulgence, inclination, and holding based on these five aggregates affected by clinging is the origin of suffering. The removal of desire and lust, the abandonment of desire and lust for these five aggregates affected by clinging is the cessation of suffering.’ 


As for the khandhas, they are merely the components of life. To help give up attachment to the khandhas, SN 22.59 explains the khandhas are unsatisfactory (cannot bring true happiness) &amp; not-self because each khandha, when examined closely, is impermanent and selfless.