The answer is "it depends"... on the voltage level, any nearby structures such as bridges, buildings, other lines that must be crossed, even the altitude. The National Electric Safety Code , which governs utility transmission lines (and not to be confused with the National Electric Code), has formulas for all of this. The particular utility and local authorities having jurisdiction may also have their own additional rules.

The photo above shows separate 220 kV, 69 kV and 12 kV lines all sharing a section of the 100'-wide corridor of the Los Angeles-San Diego dual-track main line.  In fact, these lines represent all three voltage levels of the Anaheim Public Utilities transmission and distribution system.

Taking the precedent even farther back, transmission lines and the catenary share the right-of-way in Amtrak's Northeast Corridor.  The towers are configured like a big lower case "h". The transmission line is at the top of the higher leg, and the catenary is supported by the cross part of the "H". This is the same system the Pennsylvania Railroad put there decades ago so it must work pretty well. It clearly shows that high voltage transmission and the power to the trains operating beneath can coexist. The image above shows the large amount of transmission infrastructure that can be included in the same right-of-way. Note the old lattice catenary pole and signal cross beam.