Ideas for Gift for 5 Month Old

I liked getting any kind of small toys (rattles, etc) and then hooking together a string of links and attaching the toy to the end.

Then you can hook it to the high chair and easily pick it up when it fall (including in restaurants to keep toys from hitting the dirty floor).
You can hook it to any kind of floor toy and have it hang down.
You can hook it to a car seat or, if you have a handle above the back seat in the car above the window, you can hook it there.

All kinds of possibilities. Those links are great.

Soft blocks are good for that age. No problems with putting in her mouth plus she can stack them up. And the colorful patterns will entertain her. Plus, if she gets mad and throws it, you won't get hurt. Other than that, there are toys that suction cup to the high chair.

I like the idea of the links. I used those links a lot as it enables kids to pull their toys back up (they don't hit the floor)

Because your little one is so young, I looked up "soft teething toys" on Google.
Here are some links to toys which might keep a baby busy:

http://www.amazon.com/Lamaze-Play-Rusty-Robot-Along/dp/B0...

http://www.amazon.com/Jellycat-Peek-Baby-Soft-Book/dp/B00...

http://www.amazon.com/Infantino-Big-Discovery-Cube-Develo...

http://www.amazon.com/Whoozit-Starz-Lights-Sounds-Activit...

(note, the above is not the original whoozit, so it does make some noise)

an original whoozit...
http://www.diapers.com/p/manhattan-toy-whoozit-baby-10427...

Ultimately, anything which can fit in the links is great.
and don't forget Cheerios on the high chair tray when your little one is old enough for them!

stackable cups
Cup/spoon/sippy cups

Get things that can suction cup to the high chair. Or stacking cups. One of my DD's favorites was this Baby Einstein octopus thing that played music and spoke 3 languages and taught her colors. She was 4 mo. old at her first Christmas.

I also agree that the Music Table (I think ours is Leapfrog) is an excellent choice. Can be used with or without the legs for several years.

This activity cube was one of my son's favorite toys at that age! It's perfect for right when they are learning to sit up, as it can help give them some stability - they can lean on it while they play. It has several activities to keep them busy and engaged. It's probably best on the floor, but might also work in a high chair. http://www.amazon.com/Little-Tikes-Play-Cube/dp/B008MTYTY...

Another great one is the music table. Again, perfect for a new sitter and it can grow with them - you can add legs when they are ready to stand up. I really like the Leapfrog one, but there are others out there: http://www.amazon.com/LeapFrog-Learn-Groove-Musical-Table...

There are several suction cup toys on this page that would work... the suction cup helps keep them on the tray, while giving some entertainment time...

http://www.diapers.com/html/sg/sassy-suction-cup-toy.html...