5000 rounds or pounds of ammo?

To answer your question
Some ammo is readily available some is not
22lr is next to impossible

Primers are in stock routinely but most powder is non existent

I have been told that part of the problem with shipping things like primers and powder to Alaska is the barges can only carry a set limit (I was told 400 pounds)
And since the barges are how nearly everything gets here, you are competing for space on the barge

I got curious and found this http://www.lynden.com/learn/HazMat/docs/173/49cfr173.171.pdf

§ 173.171 Smokeless powder for small arms.
Smokeless powder for small arms which has been classed in Division 1.3 may be reclassed in Division 4.1, for transportation by
motor vehicle, rail car, vessel, or cargo-only aircraft, subject to the following conditions:
(a) The powder must be examined and approved for a Division 1.3 and Division 4.1 classification in accordance with §§173.56 and
173.58 of this part.
(b) The total quantity of smokeless powder may not exceed 45.4 kg (100 pounds) net mass in:
(1) One rail car, motor vehicle, or cargo-only aircraft; or
(2) One freight container on a vessel, not to exceed four freight containers per vessel.
(c) Only combination packagings with inner packagings not exceeding 3.6 kg (8 pounds) net mass are authorized. Inner
packagings must be arranged and protected so as to prevent simultaneous ignition of the contents. The complete package must be
of the same type which has been examined as required in §173.56 of this part.
(d) Inside packages that have been examined and approved by the Associate Administrator may be packaged in UN 4G fiberboard
boxes meeting the Packing Group I performance level, provided all inside containers are packed to prevent shifting and the net
weight of smokeless powder in any one box does not exceed 7.3 kg (16 pounds).