First, multiply each side of the equation by the lowest common denominator of the two fractions which is #color(red)(40)# to eliminate the fractions while keeping the equation balanced:

#color(red)(40) xx (p - 2)/5 = color(red)(40) xx p/8#

#cancel(color(red)(40))8 xx (p - 2)/color(red)(cancel(color(black)(5))) = cancel(color(red)(40))5 xx p/color(red)(cancel(color(black)(8)))#

#8(p - 2) = 5p#

Next, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

#color(red)(8)(p - 2) = 5p#

#(color(red)(8) xx p) - (color(red)(8) xx 2) = 5p#

#8p - 16 = 5p#

Then, add #color(red)(16)# and subtract #color(blue)(5p)# from each side of the equation to isolate the #p# term while keeping the equation balanced:

#-color(blue)(5p) + 8p - 16 + color(red)(16) = -color(blue)(5p) + 5p + color(red)(16)#

#(-color(blue)(5) + 8)p - 0 = 0 + 16#

#3p = 16#

Now, divide each side of the equation by #color(red)(3)# to solve for #p# while keeping the equation balanced:

#(3p)/color(red)(3) = 16/color(red)(3)#

#(color(red)(cancel(color(black)(3)))p)/cancel(color(red)(3)) = 16/3#

#p = 16/3#