The effective rate with continuous compounding is
... R = (e^r) -1
... R = e^.05 -1 ≈ 5.1271%
The effective rate with semiannual compounding is
... R = (1 +r/2)² -1
We want these to be the same, so we want ...
... 0.051271 = (1 +r/2)² -1
... √1.051271 = 1 +r/2
... r = 2(√1.051271 -1) ≈ 5.063%
The best choice is ...
... a. 5.06%