__Solution to Problem 5:__

If tan x = opposite / adjacent = 5 = 5 / 1, then we can say that opposite = 5 and adjacent = 1 and find the hypotenuse using Pythagora's theorem.

hypotenuse^{ 2} = adjacent^{ 2} + opposite^{ 2}

hypotenuse^{ 2} = 1^{ 2} + 5^{ 2}

hypotenuse = sqrt (26)

We now use trigonometric ratios to find

sin x = opposite / hypotenuse = 5 / sqrt (26)

cos x = adjacent / hypotenuse = 1 / sqrt (26)

More references on solving problems related to trigonometry and geometry.