There are some substantial advantages to a mounted archer over a mounted HTH char.
The archer can get a full attack every round that takes place at the mid point of the movement FOR THE MOUNT! Since it is the horse moving and not the archer (mounted combat rules). So it is possible to nip into the 30' range, shoot and then move out. Which is far better than Shot on the Run. This works particularly well if the mount has Expeditious Retreat on it. Of course there are penalties for attacking while the mount is moving, but that's what the mounted combat feats are for.
By contrast, the HTH char only gets 1 attack if moving more than 5' since he has to wait until getting to the target, though he can use the charge manuver which is useless to the archer.
Mounted combat is also good for giving the archer room to work in and keeping out of AoO range, since his weapon is useful up to a substantial distance. Where as melee weapons are only good at, well melee ranges.
If you can obtain a flying mount well things just get better from there, since you can just circle your enemies and rain death on them.
At only 5th level your choices as to mounts are fairly limited I would guess (check the mount rules for Paladins in "Defenders of the Faith"). So you will probably be stuck with a heavy war horse I'd guess. I know that the 3.5e MM has expanded the range of "Cohort" monsters (Ie. from the leadership feat) that should give you a guide at least to what some other possibilities are. I would look at a Dire Wolf if you want to stick to the ground (cohort lvl of 9?) or a Griffon (cohort lv of 10). A dire wolf is probably one of the best mounts short of something really wild, they have good HD, good attacks, good extras and are generally pretty tough all around. If you go for the griffon try to make sure you can get it to go up a size class to Huge as it makes a griffon far tougher and more formidable.
One last word of caution. Mounts are fragile and will generally die from one or two good attacks from equal Party-CR opponents. So be prepaired to buff it up as much as possible and replace it, if you bring it into combat.