cut notch in stud?

I'm trying to install some electric cable just behind the baseboards so I cut out a small section behind the baseboards (which the baseboards will eventually hide) and I drilled through some studds with 5/8 for the electric cable.
There is one part of the wall where it seems to have 3 studs together, I'm not sure if that is a supporting wall or not but the drill piece I have is not long enough to drilla hole through all 3 studs.
So, I cut a small notch just at the front of the studs to feed the wire through.
Afterwards though I thought that might weaken it a bit if it was supporting so was wondering if I should fit a small piece of shim/wood block back into the notch?

 

Usually multiple studs together mean they are carrying a load. When you notch or run wiring too close to the edge you have to install a nail plate to protect it. IMO it would be better to get a longer drill bit.

 

Yeah, it's in the list but that's all I had that day. I was more worried about the notch in the edge weakening the studs but the notch is about 2cm deep - shouldn't be an issue?
Also, some of the holes I drilled were near the bottom of the studs rather than raise a bit off the floor because I only had access behind the baseboards.

 

A 5/8" hole or a small notch is not going to weaken the studs.

 

You do, however, need to add nail plates at the minimum to prevent someone hitting the cord with a nail or screw down the road.

 

Spade bits aren't just one length and they even sell extensions.