To solve this equation, we first need to combine like terms on the left side of the equation.

7 1/8 - x + 2 3/8 = 5 7/8

Convert the mixed fractions to improper fractions:

7 1/8 = 57/8
2 3/8 = 19/8

Now substitute the improper fractions back into the equation:

(57/8 - x) + 19/8 = 47/8

Combine like terms:

57/8 - x + 19/8 = 47/8
76/8 - x = 47/8

Subtract 76/8 from both sides:

-x = -29/8

Now, multiply both sides by -1 to solve for x:

x = 29/8

Therefore, the solution to the equation is x = 29/8.