See an oral surgeon
After 5 months, the
osseointegration that has occurred between your bone and the implant will make
it very difficult to remove the implant, and could have permanent effects on
your nerve that is affected. I would highly recommend that you see a skilled
oral surgeon to discuss your options, as a general dentist is not properly
equipped to handle a case such as yours.
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It IS possible to unscrew dental implants
When inserting dental implants the initial torque is often 30-50 N (newtons is a unit of force). To reverse direction and unscrew usually requires upwards to 500 N, and most dental offices do not have tools for this. If it CAN be unscrewed, that would be a better option than cutting out the implant, as the nerve that the implants are already touching/cutting will certainly become more damaged.
It is best to see an experienced oral surgeon and possibly a neurosurgeon to try to save the nerve. After 5 months it is possible that the nerve is beyond repair.
Numbness after implant placement in the maandibular canal.
To correct the numbness you will need to remove the implants but that does not guarantee the return of feeling. You may ned a neurosurgeon too reconnect the nerves and it may be too late for good results after 5 months.
You may be able to unscrew the implants or they may need to be removed with a trephine.
PROCEED WITH GREAT CAUTION TO NOT MAKE MATTERS WORSE.
Misplaced Implants With Nerve Damage
From what I can see and your narrative of the treatment you received, serious issues exist with no simple answer. You should find the most highly regarded oral surgeon in your area and have your case and options thoroughly reviewed.