Repeated consecutive values above a threshold

Question

I would like to know if a list has repeated consecutive values above a threshold. Lets say for this example the threshold is 5.

list={0, 0, 1, 2, 3, 3, 4, 2, 1, 2, 0, 2, 6, 7, 6, 5, 4, 3, 3, 4, 6, 2, 7, 6, 5, 3, 5, 4, 5, 2, 2, 1, 2, 4, 3, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 4, 3, 0, 1, 2}

because of the run 6, 7, 6, and 7, 6,the function should return True or 1 or some indication that consecutive values in the list are above the threshold.

If the threshold is 6 the function would yield False or 0 as there are no consecutive values above 6.

This code fails

Select[Split[list], First[#] > 5 && Length[#] > 1 &, Infinity]

The Split only works for consecutive values of the same value where I need it to split for consecutive values above a threshold.

I tried SplitBy but my pattern is incorrect.

SplitBy[list, Repeated[#] > 5 &]

I understand that neither of these functions above will give True or 1 but once the pattern is correct, taking it to the True or 1 is easy.

Answer 1

Fundamental operation:

t = 5;        
us = UnitStep[list - (t+1)];

(* {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, \
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} *)

Then look for sequential ones by any method:

us*list // Differences // FreeQ[1] // Not

MatchQ[us, {___, 1, 1, ___}]

Max @ ListConvolve[{1, 1}, us] > 1