4-5 months all told (i.e., including mustering of troops, supplies, the journey itself), sounds reasonable to me. Provided the army goes at about 10-20 miles per day, the journey itself should only take 1-2 months, maybe a little more.
I mean, think about it. Frodo got from Hobbiton to Rivendell (almost 500 mi.) in about a month, and he was injured half the time and almost never actually took the road. Even though there are a lot more people in this army, they will be taking the road and will be in good health, I'm assuming. I don't see how the journey itself can take more than 2 months, maybe a little more if there are any serious mishaps.
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