There are some sites dead, some still work, here a good video with detailed instructions how to replace and what to use.
E34 Dashboard Fix Dull Display / Gauges not working - Fix your BMW dashboard for 2,50 using 5 new capacitors.
Are your gages not working anymore? Or is your display not showing any numbers? A bad capacitor could be the problem.
0:05 The Problem
1:00 Cluster Disassembly
4:00 Desoldering
4:57 Old Capacitor Locations
4:59 New Capacitor Locations
5:00 Soldering
6:42 Solder Varnish
6:50 Assembly

Parts used:
2 X 22F 62V
3 X 220F 25V

This might also work for BMW E30 (3-series), BMW E32 (7-series), BMW E34(5-series) My car: 1989 BMW E34 525i M20B25

Capacitor Replacement Tutorial voltage shown on the capacitor is the max voltage rating it can handle before the capacitor explodes, as you normally have 13.xxV on a car, 35V should be fine, 63v has a bigger safety margin

more DIY

Trevor M mentioned:

Four things you need to consider when ordering new caps.
- The value of the cap should match or exceed the original. For example a 220uF cap should be replaced with a 220uF cap or a 470uF would work too if you couldn't find a 220uF. What I'm saying, it's ok to go greater value, not less.
- The voltage rating of the replacement capacitor must be equal to or greater than the original. For automotive use, a 25v or 35v capacitor will be fine.
- Capacitors have a temperture rating of either 85 or 105 degrees C. Obviously, the 105 deg caps are better suited for service where there are high temperatures and will last longer than the 85 deg caps. They cost a bit more.
- The physical size. They must be the same size or smaller to fit the board.