B737NG Captain reported encountering wake turbulence on approach to LAX in trail of a B787.

Narrative

SOCAL Approach Control cleared our flight for the ILS 24R via the CRCUS transition. We were following a B787-9. To help increase the space between our airplanes the Los Angeles Center Controller instructed us to slow to 250 KIAS while on the ANJLL4 arrival which we complied with. Looking at our TCAS display; I estimated the 787 was approximately 5 miles ahead of us.SOCAL approach appropriately cautioned us for wake turbulence since we were following the heavy 787. Our flight was normal until we reached CRCUS waypoint where we encountered the 787's wake.The wake encounter was significant and the airplane rapidly rolled and yawed to approximately 25 degrees of right bank even with my approximately 3/4 deflection aileron correction. The wake encounter concerned me enough to where I verbalized and initiated the upset recovery (push; roll; thrust; etc.) procedure. The airplane continued to bank rapidly and dutch-roll to the right for several more moments before we flew out of the wake and control returned to normal. During the recovery procedure we momentarily deviated from the lateral and vertical path for the approach.Due to frequency congestion we did not make a report to SOCAL ATC.We flew in and out of the 787's wake for a several minutes although we did not experience any rapid bank movements like we did at CRCUS. Our flight landed normally behind the 787.