Given that the next word should start with the ending two letters of the previous word. From this,
The first word is
SHIVER
Now, the next word should start with ER and must contain OT in the middle.
EROTIC
Now, the next word should start with IC and must contain IC in the middle.
ICICLE
Now, the next word should start with LE and must contain NG in the middle.
LENGTH
Now, the next word should start with TH and must contain RA in the middle.
THRASH
Hence, the required five words are SHIVER, EROTIC, ICICLE, LENGTH, THRASH.