Reduce : This system cannot be solved with the methods available to Reduce

I have a few expressions and need to get a final simplified (reduced,solved) results. I am new and tried/searched different ways for my problem but couldn’t find the reason. These are my expressions:

R0 = FractionalPart[Log[5, x + (3/ 4)]] ==  FractionalPart[Log[5, xP + (3/ 4)]]
R1  = Log[5, xP + (3 / 4)] - Log[3, yP + ( 5 / 2)] == Log[5, x + (3 / 4)] - Log[3, y + ( 5 / 2)]
F = ( (x == xP && y == yP) || ( Exists[{xPP, yPP},  xPP < yPP && xP == 5 xPP + 3 && yP == 3 yPP + 5]))
R = R0 && R1 && F
Reduce[R && xP >= yP , {x, y, xP, yP}, Reals]

when I run this it takes a long time and seems infinite loop or something and never finishes. I also tried this

Reduce[R , Element[{x, y, xP, yP}, Reals]]

and it returns the error: Reduce : This system cannot be solved with the methods available to Reduce
We expect two functions for xP and yP based on x and y, for each. I am sure there must be a final reduce for this problem because there was a code for it before, but we don’t have that code at this moment, so I think my transformation to Mathematica MUST be wrong. Please help me through this.

2- How can I make sure that each single expression is error free?
Thanks a lot

EDITED : this new gives me an error, "This system cannot be solved with the methods available to Solve" does someone know why ?

Solve[FractionalPart (Log[5, x + (3/4)]) == FractionalPart (Log[5, X + (3/4)]) && 
Log[5, x + (3/4)] - Log[3, y + (5/2)] == Log[5, X + (3/4)] - Log[3, Y + (5/2)] &&
    ((x == X && y == Y)||(x < y && (X - 3)/5 < (Y - 5)/3)) && X >= Y,{X,Y}, Integers]