While I am a bit out of date I believe the 50' and 35' as stated by 'Escape path' rather than the 35' and 15' put forward by aterpster. Perhaps these numbers are used in another part of the world?
50 ft screen dates back to the very early days of the US regulators. According to a chap of great antiquity who was a young fellow back in the early post-earliest days of the regulator (probably no longer with us - he related the tale on a course I attended about 20 years ago), the story was that it derived from a military demonstration into a parade ground surrounded by (about) 50ft high trees ..
That figure was then adopted in the civil world. Subsequently, it remained the requirement for lighties both for takeoff and landing. However, as I recall at the time that the ICAO PAMC came into vogue (early F27 days) the takeoff screen for heavies reduced to 35ft, where it remains today.
Very much later, with the introduction of a degree of formalised discipline with respect to contaminated runway operations, there arose a permission to use a reduced screen of 15ft for such calculations.
As an aside, aterpster is quite expert in these operational matters ...
The five or ten minute limits for max thrust relate to factors regarding the long term life of the engine.
That may well be true. However, the certificated (read legal) limit at takeoff thrust is either 5 or 10 minutes according to the Type.