Do Thorncaster Sliver's triggered abilities go on the stack?
Triggered abilities always use the stack. That includes Thorncaster Sliver's and Hellrider's.


  112.3c Triggered abilities have a trigger condition and an effect. They are written as "[Trigger condition], [effect]," and include (and usually begin with) the word "when," "whenever," or "at." Whenever the trigger event occurs, the ability is put on the stack the next time a player would receive priority and stays there until it's countered, it resolves, or it otherwise leaves the stack.


Here's what happens:


You attack with five slivers. Five instances of Thorncaster Sliver's ability triggers
You place the abilities on the stack in the order of your choice: (Best order used)

You place PS#1's ability on the stack targeting the 2/2
You place PS#2's ability on the stack targeting the 2/2
You place TS's ability on the stack targeting the Blood Artist
You place MS#1's ability on the stack targeting your opponent
You place MS#2's ability on the stack targeting your opponent

MS#2's ability resolves:

Deal one damage to your opponent.

MS#1's ability resolves:

Deal one damage to your opponent.

TS's ability resolves:

Deal one damage to the Blood Artist

The Blood Artist dies. Blood Artist's ability triggers.
Your opponent places Blood Artist's ability on the stack targeting you.
Blood Artist's ability resolves:

You lose one life.
Your opponent gains one life.

PS#2's ability resolves:

Deal one damage to the 2/2.

PS#2's ability resolves:

Deal one damage to the 2/2.

The 2/2 dies.
[Move on the Declare Blockers]


Result:


The Blood Artist and the 2/2 died.
The opponent's life went down 2, then went up 1.
Your life went down 1.