Do not jump to the solved board yet. Try a few more deductions first; if you are stuck, click View hint.
A Horse With No Name Murdoku coordinate map - columns C1-C6 and rows R1-R6
Coordinate note: R1 means row 1, C1 means column 1, and C5R3 means column 5, row 3.
The outlaw clue points straight to the horse at C5R3. Once that square is reserved, every other cell in R3 and C5 can be ruled out. Now ask who can actually stand on that outlaw horse square. A, B, D, and E all conflict with their own clues there, so C is the only suspect that fits C5R3. With C fixed, A must still be beside a cactus and south of C. Only one cell satisfies both conditions, so A is forced to C6R5. That placement leaves only one usable table-adjacent square for D. After D is placed, B is reduced to the remaining square on the same diagonal as A. Only one boulder-adjacent square remains for E. Once E takes it, V goes in the final open square and the full board is determined.
All hint layers are open. Use the solved board only to check your final placement.
A Horse With No Name Murdoku solution - solved board