For my new conlang Çirkhin Khena, the numbers are

Khirtu-ხირთუ-1
Ark'-არკ-2
Sağ-საღ-3
Otijj-ოთიჯ-4
Khun-ხუნ-5
Ik'se-იკსე-6
Shq'idi-შყიდი-7
Rq'a-რყა-8
P'hara-პჰარა-9
Uti-უთი-10

Unusual, but not inconceivable. What's the basis for evolution of 25?

Well, I wanted to make the numbers short and easy to pronounce, so I decided on a base-50, but I couldnt think of that many numbers, so Idid a base-25.

Here are numbers 1-10 in N'ketle.

1 uch
2 ucho, otso
3 uchotso, uchos, ofo
4 otsus
5 ofus
6 soso
7 fotso, foso
8 sosus
9 fuso
10 suso

I may already have answered, but whatever I posted is probably out of date. Here are the Tikolmian numbers from 1 to 10 (a):
1 - iso
2 - mik
3 - zekō
4 - tiek
5 - tab
6 - lad
7 - sobok
8 - ayw
9 - sas
a - mos

We use base 11. I'll be back in a little with the numbers in Conilan and Erian.

Conilan (base 10):
un - 1
dos - 2
tres - 3
quatro - 4
cinco - 5
sis - 6
sete - 7
oto - 8
novo - 9
dis - 10

Erian (base 13):
unea - 1
deaw - 2
traois - 3
catrae - 4
seinc - 5
seise - 6
septae - 7
neawf - 9
deis - a

Should have been:
unea - 1
deaw - 2
traois - 3
catra - 4
senc - 5
seise - 6
sep - 7
wit - 8
neawf - 9
deis - a

I forgot 8

Here's a sample from my upcoming conlang d'Euscadia ri'tamire. Here are the number and they traditionally go from 1 to 10 (A). An example of base-11 system that is. Take note that the number names are in ancient forms. I will reveal the modern names when I am making the proper thread about the language. The modern forms are similar to the ones presented here so you are not really missing anything important.

0: deunar

1: tulawam

2: ramsa

3: rivarsa

4: savat

5: gomersa

6: harse

7: valabo

8: tenarif

9: ra'melis

10 (A): tu'melis

11: melis'tulawam

12: melis'tulatula

13: melis'tularam

14: melis'tularivar

Hopefully you get the idea.

Yay, someone else who uses funny prime numbers for number bases!
Just stopping by to give everyone the new Erian numbers. Or, should I say, the Llyffws numbers, as that's the name of this dialect of Erian. It's also known as "Welsh Erian", as opposed to "Irish Erian".
1 - yn
2 - dw
3 - trei
4 - catra
5 - senc
6 - sis
7 - sep
8 - yt
9 - nwff
10/a - dis

Llyffws actually uses a mixed-base system. The numbers from 1 to 15 are what you'd expect from a Romance language, but the numbers from 15 to 20 are base 15-looking, and after 20 I don't know what happens. All I know is that thirty is called two fifteens.
*goes back into hiding to work on essays*

In Kholi, a base 5 system exists:

1 - mila
2 - tupa
3 - xi
4 - rhau
5 - peta
-
6 - pemla
7 - patpa
8 - pehi
9 - perhau
10 - tupata
11 - tupatamla
12 - tupatatpa
13 - tupatehi
14 - tupatrhau
15 - xipeta
16 - xipetemla
20 - rhaupata
21 - rhaupatamla
22 - rhaupatatpa
23 - rhaupatehi
24 - rhaupatrhau
25 - pe(t)peta
50 - tupepeta
75 - xipepeta
100 - rhaupepeta
125, or a large number - khilou

But in my other conlang, there is a vigesimal system with sub-base 10...
əħɾ
1 kok
2 sek
3 kɾət
4 ħo
5 pei
6 sakel
7 sodək
8 jip
9 on
10 get
11 get o kok
12 get o sek
15 get o pei
20 ħatti
400 ħattatti
972 sekħattatti o jipħatti o get o sek
(800 + 160 + 10 + 2)