2sin^x + 5cosx + 1 = 0

2-2cos²x+5cosx+1=0

3-2cos²x+5cosx=0

2cosx²-5cosx-3=0  |cosx|<=1

cosx=t    2t²-5t-3=0   t=(5+-7)/4  t1=3  t2=-1/2

cosx=-1/2

x=2П/3+2Пk

x=4П/3+2Пk