First off - this is a strictly incredible mental image. I hope you keep writing Mr. 5’s ideas down!
Unfortunately, there’s no indication that our universe is in any way tiger-shaped. The Universe seems to be almost exactly flat in every direction - which means that if we were to get a spaceship with infinite fuel and shoot off in one direction, we would never loop back on ourselves or find the edge of the tiger; we’d just see a lot of universe that looks pretty similar to the portion of the universe we can see from the Earth.
(As a further note- as far as we know, the only dinosaurs that have ever existed were here on Earth. It’d be quite a shock to find more dinosaur bones elsewhere in the universe.)
“What’s outside the Universe” is actually a really hard question to answer, because language often gets tangled up and in the way. The Universe is defined as everything that exists - all the matter, and light, and dark matter - all the stuff that makes planets and people, and all the energy and the space between them. Within the Universe is the only region where “space” and “time” have any meaning.
The second complication is that it’s not mathematically clear whether or not the universe is finite in space. If it is infinitely large, the concept of “outside” the universe means even less - since there’s galaxies and planets for an infinite distance no matter which way you go. There’s no indication that there are fewer galaxies in any given direction, which you might expect if the universe had an edge, or stopped somehow. Often we just assume that the Universe is infinite in all directions because it makes it slightly less mindbendy.
So, (tragically) no space tigers or space dinosaurs, just an awful lot of galaxies.